chapter 9 resource masters - mhschooliv teacher’s guide to using the chapter 9 resource masters...

Chapter 9Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission isgranted to reproduce the material contained herein on the condition that suchmaterial be reproduced only for classroom use; be provided to students, teachers,and families without charge; and be used solely in conjunction with GlencoeCalifornia Mathematics, Grade 6. Any other reproduction, for use or sale, isprohibited without prior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

ISBN: 978-0-07-878304-3MHID: 0-07-878304-6 CAGR6 CRM9

Printed in the United States of America

4 5 6 7 8 9 10 MAL 14 13 12 11 10 09

Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters

booklets are available as consumable workbooks in both English and Spanish.

MHID ISBNStudy Guide and Intervention Workbook 0-07-878871-4 978-0-07-878871-0

Skills Practice Workbook 0-07-878873-0 978-0-07-878873-4

Practice Workbook 0-07-878875-7 978-0-07-878875-8

Word Problem Practice Workbook 0-07-878877-3 978-0-07-878877-2

Spanish VersionsStudy Guide and Intervention Workbook 0-07-878872-2 978-0-07-878872-7Skills Practice Workbook 0-07-878874-9 978-0-07-878874-1Practice Workbook 0-07-878876-5 978-0-07-878876-5Word Problem Practice Workbook 0-07-878878-1 978-0-07-878878-9

Answers for Workbooks The answers for Chapter 9 of these workbooks can be found in the

back of this Chapter Resource Masters booklet.

StudentWorks Plus™ This CD-ROM includes the entire Student Edition test along with the

English workbooks listed above.

TeacherWorks Plus™ All of the materials found in this booklet are included for viewing,

printing, and editing in this CD-ROM.

Spanish Assessment Masters MHID: 0-07-878879-X ISBN: 978-0-07-878879-6

These masters contain a Spanish version of Chapter 9 Test Form 2A and Form 2C.

iii

Teacher’s Guide to Using the Chapter 9 Resource Masters .........................................iv

Chapter Resources Chapter 9 Student-Built Glossary ......................1Chapter 9 Family Letter (English) ......................3Chapter 9 Family Activity (English) ....................4Chapter 9 Family Letter (Spanish) .....................5Chapter 9 Family Activity (Spanish)...................6Chapter 9 Anticipation Guide (English)..............7Chapter 9 Anticipation Guide (Spanish) ............8

Lesson 9-1 Simple EventsLesson Reading Guide ......................................9Study Guide and Intervention ..........................10Skills Practice...................................................11Practice ............................................................12Word Problem Practice ....................................13Enrichment .......................................................14

Lesson 9-2 Sample SpacesLesson Reading Guide ....................................15Study Guide and Intervention ..........................16Skills Practice...................................................17Practice ............................................................18Word Problem Practice ....................................19Enrichment .......................................................20

Lesson 9-3 The FundamentalCounting PrincipleLesson Reading Guide ....................................21Study Guide and Intervention ..........................22Skills Practice...................................................23Practice ............................................................24Word Problem Practice ....................................25Enrichment .......................................................26

Lesson 9-4 PermutationsLesson Reading Guide ....................................27Study Guide and Intervention ..........................28Skills Practice...................................................29Practice ............................................................30Word Problem Practice ....................................31Enrichment .......................................................32TI-83/84 Plus Activity .......................................33

Lesson 9-5 CombinationsLesson Reading Guide ....................................34Study Guide and Intervention ..........................35Skills Practice...................................................36Practice ............................................................37Word Problem Practice ....................................38Enrichment .......................................................39TI-83/84 Plus Activity .......................................40

Lesson 9-6 Problem-SolvingInvestigation: Act It OutStudy Guide and Intervention ..........................41Skills Practice...................................................42Practice ............................................................43Word Problem Practice ....................................44

Lesson 9-7 Theoretical andExperimental ProbabilityLesson Reading Guide ....................................45Study Guide and Intervention ..........................46Skills Practice...................................................47Practice ............................................................48Word Problem Practice ....................................49Enrichment .......................................................50TI-83/84 Activity ...............................................51

Lesson 9-8 Compound EventsLesson Reading Guide ....................................52Study Guide and Intervention ..........................53Skills Practice...................................................54Practice ............................................................55Word Problem Practice ....................................56Enrichment .......................................................57TI-73 Activity ....................................................58

Chapter 9 AssessmentStudent Recording Sheet ................................59Rubric for Scoring Pre-AP................................60Chapter 9 Quizzes 1 and 2 ..............................61Chapter 9 Quizzes 3 and 4 ..............................62Chapter 9 Mid-Chapter Test .............................63Chapter 9 Vocabulary Test ...............................64Chapter 9 Test, Form 1 ....................................65Chapter 9 Test, Form 2A..................................67Chapter 9 Test, Form 2B..................................69Chapter 9 Test, Form 2C..................................71Chapter 9 Test, Form 2D..................................73Chapter 9 Test, Form 3 ....................................75Chapter 9 Extended-Response Test ................77Chapter 9 Standardized Test Practice..............78Unit 4 Test ........................................................81

Answers..................................................A1–A37

Contents

iv

Teacher’s Guide to Using the Chapter 9 Resource Masters

The Chapter 9 Resource Masters includes the core materials needed for Chapter 9. Thesematerials include worksheets, extensions, and assessment options. The answers for thesepages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing on theTeacherWorks Plus™ CD-ROM.

Chapter ResourcesStudent-Built Glossary (pages 1–2) Thesemasters are a student study tool thatpresents up to twenty of the key vocabularyterms from the chapter. Students are torecord definitions and/or examples for eachterm. You may suggest that studentshighlight or star the terms with which theyare not familiar. Give this to students beforebeginning Lesson 9-1. Encourage them toadd these pages to their mathematics studynotebooks. Remind them to complete theappropriate words as they study each lesson.

Family Letter and Family Activity(pages 3–6) The letter informs yourstudents’ families of the mathematics theywill be learning in this chapter. The familyactivity helps them to practice problems thatare similar to those on the state test. A fullsolution for each problem is included.Spanish versions of these pages are alsoincluded. Give these to students to takehome before beginning the chapter.

Anticipation Guide (pages 7–8) Thismaster, presented in both English andSpanish, is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.

Lesson ResourcesLesson Reading Guide Get Ready for theLesson reiterates the questions from thebeginning of the Student Edition lesson.Read the Lesson asks students to interpretthe context of and relationships amongterms in the lesson. Finally, RememberWhat You Learned asks students tosummarize what they have learned usingvarious representation techniques. Use as astudy tool for note taking or as an informalreading assignment. It is also a helpful toolfor ELL (English Language Learners).

Study Guide and Intervention Thismaster provides vocabulary, key concepts,additional worked-out examples and CheckYour Progress exercises to use as areteaching activity. It can also be used inconjunction with the Student Edition as aninstructional tool for students who havebeen absent.

Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.

Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for second-day teaching of the lesson.

v

Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.

Enrichment These activities may extendthe concepts of the lesson, offer an historicalor multicultural look at the concepts, orwiden students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.

Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts insome lessons of this chapter. Use as analternative approach to some concepts or asan integral part of your lesson presentation.

Assessment OptionsThe assessment masters in the Chapter 9Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final) assessment.

Student Recording Sheet This mastercorresponds with the standardized testpractice at the end of the chapter.

Pre-AP Rubric This master providesinformation for teachers and students onhow to assess performance on open-endedquestions.

Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.

Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice and free-response questions.

Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 10 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.

Leveled Chapter Tests• Form 1 contains multiple-choice questions

and is intended for use with below gradelevel students.

• Forms 2A and 2B contain multiple-choicequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.

• Form 3 is a free-response test for use withabove grade level students.

All of the above mentioned tests include afree-response Bonus question.

Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.

Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and short-answer free-response questions.

Answers• The answers for the Anticipation Guide

and Lesson Resources are provided asreduced pages with answers appearing in red.

• Full-size answer keys are provided for theassessment masters.

Chapter 9 1 Glencoe California Mathematics, Grade 6

Vocabulary TermFound

Definition/Description/Exampleon Page

combination

complementary event

composite event

experimental probability

fair game

Fundamental Counting Principle

independent event

outcome

permutation

NAME ________________________________________ DATE ______________ PERIOD _____

Student-Built Glossary

Ch

apte

r R

eso

urc

esThis is an alphabetical list of new vocabulary terms you will learn inChapter 9. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.

9C

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.


Vocabulary TermFound

Definition/Description/Exampleon Page

probability

random

sample space

simple event

theoretical probability

tree diagram

NAME ________________________________________ DATE ______________ PERIOD _____

Student-Built Glossary9C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

Family LetterNAME ________________________________________ DATE ______________ PERIOD _____


Dear Parent or Guardian:

Probability is used in such diverse areas as weather forecasting,

business, and genetics. We use combinations and permutations

to determine the number of possible outcomes in a given

situation. This type of information helps us to decide how to

spend our money or to predict the color of a puppy,s fur.

In Chapter 9, Probability, your child will learn probability, simple

events, sample spaces, the fundamental counting principle,

permutations, combinations, theoretical and experimental

probability, and independent events. Your child will also learn the

problem solving strategy of acting it out. In the study of this

chapter, your child will complete a variety of daily classroom

assignments and activities and possibly produce a chapter project.

By signing this letter and returning it with your child, you agree

to encourage your child by getting involved. Enclosed is an

activity you can do with your child that practices how the math

we will be learning in Chapter 9 might be tested. You may

also wish to log on to ca.gr6math.com for self-check quizzes

and other study help. If you have any questions or comments,

feel free to contact me at school.

Sincerely,

Signature of Parent or Guardian ______________________________________ Date ________

9C

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.

Ch

apte

r R

eso

urc

es

Family ActivityStandards Practice

NAME ________________________________________ DATE ______________ PERIOD _____


1. Joshua is playing a game with hisfriends. The object of the game is to geta sum of 9 when two standard numbercubes are rolled.

How many possible ways are there forrolling two number cubes? How many ofthese ways have a sum of 9?

A 36 ways; 4 with a sum of 9B 36 ways; 8 with a sum of 9C 16 ways; 4 with a sum of 9D 16 ways; 8 with a sum of 9

Fold here.

Solution1. Since there are 6 possible outcomes for

each number cube, there are 6 � 6 or 36 possible rolls.

In order for the sum of the numbercubes to be 9, we can have the followingcombinations:

There are 4 possible combinations thatwill result in a sum of 9.

The answer is A.

2. Justine is designing a probabilityexperiment in which she can simulatefinding the probability of getting snowovernight if the weatherman said thatthere is a 25% chance that theprecipitation overnight will be rain, a50% chance that the precipitation willbe snow, and a 25% chance that therewill be no precipitation at all.

Which of the following would bestsimulate what might happen overnight?A toss a coinB spin a spinner with four equal

sectionsC roll a standard number cubeD pick from 25 marbles in a bag

Solution2. Hint: Consider the number of outcomes

possible and consider their probabilitiesas fractions of a whole.

The probabilities can all be expressed in

terms of �14

�. Choice B is the only option

that represents fourths.

The answer is B.

9

Fold the page along the dashed line. Work each problem on another piece of paper.Then unfold the page to check your work.

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.Cube 1 Cube 2

3 66 34 55 4

51

432

1

Carta a la familiaNOMBRE ______________________________________ FECHA ____________ PERÍODO ___

Capítulo 9 5 Glencoe California Mathematics, Grade 6

Estimado padre o apoderado:

La probabilidad se usa en áreas tan diversas como el pronóstico

del tiempo, los negocios y la genética. Usamos combinaciones y

permutaciones para determinar el número de posibles resultados

en una situación dada. Este tipo de información nos ayuda a

decidir cómo gastar nuestro dinero o predecir el color del pelaje

de un cachorro.

En el Capítulo 9, Probabilidad, su hijo(a) aprenderá sobre

probabilidad, eventos simples, espacios muestrales, el principio fun-

damental de conteo, permutaciones, combinaciones, probabilidad

teórica y experimental y eventos independientes. Su hijo(a) tam-

bién aprenderá la estrategia de solución de problemas mediante

simulacros. En el estudio de este capítulo, su hijo(a) completará

una variedad de tareas y actividades diarias y es posible que tra-

baje en un proyecto del capítulo.

Al firmar esta carta y devolverla con su hijo(a), usted se com-

promete a ayudarlo(a) a participar en su aprendizaje. Junto con

esta carta, va incluida una actividad que puede realizar con

él(ella) y la cual practica lo que podrían encontrar en las prue-

bas de los conceptos matemáticos que aprenderán en el

Capítulo 9. Además, visiten ca.gr6math.com para ver

autocontroles y otras ayudas para el estudio. Si tiene cualquier

pregunta o comentario, por favor contácteme en la escuela.

Cordialmente,

Firma del padre o apoderado ________________________________________ Fecha ______

9C

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.

Ch

apte

r R

eso

urc

es

Actividad en familiaPráctica de estándares

NOMBRE ______________________________________ FECHA ____________ PERÍODO ___


1. Joshua está jugando con sus amigos. Elobjeto del juego es obtener una suma de9 al lanzar dos cubos numeradosestándares.

¿Cuántas maneras posibles hay delanzar dos cubos numerados? ¿Cuántasde éstas suman 9?

A 36 maneras; 4 suman 9B 36 maneras; 8 suman 9C 16 maneras; 4 suman 9D 16 maneras; 8 suman 9

Doblen aquí.

Solución1. Puesto que existen 6 resultados posibles

para cada cubo numerado, hay 6 � 6 ó 36 tiros posibles.

Para lograr que la suma de los cubosnumerados sea 9, se tienen lascombinaciones siguientes:

Hay 4 combinaciones posibles queresultarán en una suma de 9.

La respuesta es A.

2. Justine diseña un experimento deprobabilidades en donde puede simularla búsqueda de la probabilidad de quenieve durante la noche, si el meteoró-logo dijo que hay un 25% de probabili-dad de que la precipitación sea lluvia,un 50% de que la precipitación seanieve y un 25% de que no ocurraprecipitación alguna.

¿Cuál de los siguientes simularía mejorlo que puede ocurrir durante la noche?A lanzar una moneda al aireB girar un girador de cuatro secciones

igualesC lanzar un cubo numerado estándarD escoger de entre 25 canicas en una

bolsa

Solución2. Ayuda: Consideren el número de

resultados posibles y consideren susprobabilidades como fracciones de untodo.

Las probabilidades pueden expresarse en

términos de �14

�. La opción B es la única

que representa cuartos.

La respuesta es B.

Cubo 1 Cubo 23 66 34 55 4

51

432

1

9

Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

NAME ________________________________________ DATE ______________ PERIOD _____

Anticipation GuideProbability


Ch

apte

r R

eso

urc

es

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9

Before you begin Chapter 9

• Read each statement.

• Decide whether you Agree (A) or Disagree (D) with the statement.

• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 9

• Reread each statement and complete the last column by entering an A or a D.

• Did any of your opinions about the statements change from the first column?

• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.

Step 2

Step 1

STEP 1 Statement STEP 2A, D, or NS A or D

1. The probability of an event happening is a ratio that compares the number of favorable outcomes to the number of unfavorable outcomes.

2. If the probability of an event happening is �35

� then it is more likely for the event to happen than to not happen.

3. In a probability experiment, a tree diagram can be used to show all the possible outcomes.

4. The Fundamental Counting Principle states that the number of possible outcomes can also be found by division.

5. To find the value of 4!, add 4 � 3 � 2 � 1.

6. In a combination, choosing event A then event B would be the same as choosing event B then event A.

7. The experimental probability of an event happening will always be close to the theoretical probability of that event happening.

8. The act it out strategy is a good way to solve problems because the results will be the same every time the experiment is repeated.

9. A compound event consists of two or more simple events.10. The probability of two independent events is found the same

way as the probability of two dependent events.

NOMBRE ______________________________________ FECHA ____________ PERÍODO ___

Ejercicios preparatoriosProbabilidad


Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

9

PASO 2

Antes de comenzar el Capítulo 9

• Lee cada enunciado.

• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.

• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a).

Después de completar el Capítulo 9

• Vuelve a leer cada enunciado y completa la última columna con una A o una D.

• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?

• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.

PASO 1

PASO 1 PASO 2A, D o NS

EnunciadoA o D

1. La probabilidad de que ocurra un evento es una razón que compara el número de resultados favorables con el número de resultados desfavorables.

2. Si la probabilidad de que ocurra un evento es �35

�, entonces es más probable que ocurra el evento a que no ocurra.

3. En un experimento de probabilidad, se puede usar undiagrama de árbol para mostrar todos los resultados posibles.

4. El principio fundamental de contar establece que el número po-sible de resultados puede también calcularse mediante división.

5. Para calcular el valor de 4!, suma 4 � 3 � 2 � 1.

6. En una combinación, escoger el evento A y después el evento B sería igual a escoger el evento B y después el evento A.

7. La probabilidad experimental de que ocurra un evento siempre será cercana a la probabilidad teórica de que ocurra dicho evento.

8. La estrategia de hacer un simulacro es una buena forma de resolver problemas porque los resultados serán los mismos cada vez que se repita el experimento.

9. Un evento compuesto consta de dos o más eventos simples.10. La probabilidad de dos eventos independientes se encuentra

de la misma manera que la probabilidad de dos eventos dependientes.

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Less

on

9–1


Get Ready for the LessonRead the introduction at the top of page 460 in your textbook. Writeyour answers below.

1. What fraction of the taffy is vanilla? Write in simplest form.

2. Suppose you take one piece of taffy from the box without looking. Areyour chances of picking vanilla the same as picking root beer? Explain.

Read the LessonUse the information from the introduction to answer Exercises 3–5.

3. How do you read P(cherry)?

4. P(cherry) � �468�

; where does the 6 come from? Where does the 48 come

from?

5. Probability can be written as a fraction, a decimal, or a percent. WriteP(cherry) as a decimal.

6. If there is a 25% chance that something will happen, what is the chancethat it will not happen? What are these two events called?

Remember What You Learned7. Write the equation P(A) � P(not A) � 1 in words. What does it mean with

respect to event A?

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideSimple Events

9-1 6SDAP3.3

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionSimple Events


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-1

What is the probability of rolling a multiple of 3 on a number cubemarked with 1, 2, 3, 4, 5, and 6 on its faces.

P(multiple of 3) �

� �26� Two numbers are multiples of 3: 3 and 6.

� �13� Simplify.

The probability of rolling a multiple of 3 is �13� or about 33.3%.

What is the probability of not rolling a multiple of 3 on a numbercube marked with 1, 2, 3, 4, 5, and 6 on its faces?

P(A) � P(not A) � 1

�13� � P(not A) � 1 Substitute �

13

� for P(A).

��13� ��

13� Subtract �

13

� from each side��

P(not A) � �23� Simplify.

The probability of not rolling a multiple of 3 is �23� or about 66.7%.

A set of 30 cards is numbered 1, 2, 3, …, 30. Suppose you pick a card atrandom without looking. Find the probability of each event. Write asa fraction in simplest form.

1. P(12) 2. P(2 or 3)

3. P(odd number) 4. P(a multiple of 5)

5. P(not a multiple of 5) 6. P(less than or equal to 10)

multiples of 3 possible��total numbers possible

The probability of a simple event is a ratio that compares the number of favorable outcomes to thenumber of possible outcomes. Outcomes occur at random if each outcome occurs by chance.

Two events that are the only ones that can possibly happen are complementary events. The sum ofthe probabilities of complementary events is 1.

Example 1

Example 2

6SDAP3.3

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeSimple Events


Less

on

9–1

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-1

A set of 12 cards is numbered 1, 2, 3, …12. Suppose you pick a card atrandom without looking. Find the probability of each event. Write asa fraction in simplest form.

1. P(5) 2. P(6 or 8)

3. P(a multiple of 3) 4. P(an even number)

5. P(a multiple of 4) 6. P(less than or equal to 8)

7. P(a factor of 12) 8. P(not a multiple of 4)

9. P(1, 3, or 11) 10. P(a multiple of 5)

The students at Job’s high schoolwere surveyed to determine theirfavorite foods. The results areshown in the table at the right.Suppose students were randomlyselected and asked what theirfavorite food is. Find the probabilityof each event. Write as a fraction insimplest form.

11. P(steak) 12. P(spaghetti)

13. P(cereal or seafood) 14. P(not chow mein)

15. P(pizza) 16. P(cereal or steak)

17. P(not steak) 18. P(not cereal or seafood)

19. P(chicken) 20. P(chow mein or spaghetti)

Favorite Food Responsespizza 19steak 8chow mein 5seafood 4spaghetti 3cereal 1

6SDAP3.3

A set of cards is numbered 1, 2, 3, … 24. Suppose you pick a card atrandom without looking. Find the probability of each event. Write asa fraction in simplest form.

1. P(5) 2. P(multiple of 4) 3. P(6 or 17)

4. P(not equal to 15) 5. P(not a factor of 6) 6. P(odd number)

COMMUNITY SERVICE The table shows the students involved incommunity service. Suppose one student is randomly selected torepresent the school at a state-wide awards ceremony. Find theprobability of each event. Write as a fraction in simplest form.

7. P(boy) 8. P(not 6th grader)

9. P(girl) 10. P(8th grader)

11. P(boy or girl) 12. P(6th or 7th grader)

13. P(7th grader) 14. P(not a 9th grader)

MENU A delicatessen serves different menu items, of which 2 aresoups, 6 are sandwiches, and 4 are salads. How likely is it for eachevent to happen if you choose one item at random from the menu?Explain your reasoning.

15. P(sandwich) 16. P(not a soup) 17. P(salad)

18. NUMBER CUBE What is the probability of rolling an even number or a prime number on a number cube? Write as a fraction in simplest form.

19. CLOSING TIME At a convenience store there is a 25% chance a customerenters the store within one minute of closing time. Describe thecomplementary event and find its probability.

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeSimple Events


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-1

Community Servicegirls 15boys 256th graders 207th graders 88th graders 12

6SDAP3.3

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticeSimple Events


Less

on

9–1

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-1

COINS Susan opened her piggy bank and countedthe number of each coin. The table at the rightshows the results. For Exercises 1–3, assume thatthe coins are put in a bag and one is chosen atrandom.

1. What is the probability that a quarteris chosen?

2. What is the probability that a nickel ora dime is chosen?

3. What is the probability that the chosencoin is worth more than 5 cents?

4. NUMBER CUBES Juan has two numbercubes, each with faces numbered 1, 2, …6. What is the probability thathe can roll the cubes so that the sum ofthe faces showing equals 11?

5. SKATEBOARDS Carlotta bought a newskateboard for which the probability ofhaving a defective wheel is 0.015. Whatis the probability of not having adefective wheel?

6. CALCULATORS Jake’s teacher had 6calculators for 28 students to use. If thefirst students to use the calculators arechosen at random, what is theprobability that Jake will get one?

7. VEHICLES The rental car company had14 sedans and 8 minivans available torent. If the next customer picks avehicle at random, what is theprobability that a minivan is chosen?

8. MUSIC Tina has 16 pop CDs,6 classical, and 2 rock. Tina chooses aCD at random. What is the probabilityshe does not choose a classical CD?

Coin Numberquarters 15

dimes 21

nickels 22

pennies 32

6SDAP3.3

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-1

Coin-Tossing ExperimentsIf a coin is tossed 3 times, there are 8 possible outcomes. They are listed in thetable below.

Once all the outcomes are known, the probability of any event can be found.For example, the probability of getting 2 heads is �

38�. Notice that this is the

same as getting 1 tail.

1. A coin is tossed 4 times. Complete this chart to show the possibleoutcomes.

2. What is the probability of getting all tails?

3. Now complete this table. Make charts like the one in Exercise 1 to helpfind the answers. Look for patterns in the numbers.

4. What happens to the number of outcomes? the probability of all tails?

Number of Heads 0 1 2 3

Outcomes TTT HTT HHT HHH

THT THH

TTH HTH

Number of Heads 0 1 2 3

Outcomes TTTT

4

Number of Coin Tosses 2 3 4 5 6 7 8

Total Outcomes

Probability of Getting AllTails

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading Guide Sample Spaces


Less

on

9–2

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-2

Get Ready for the LessonComplete the Mini Lab at the top of page 465 in your textbook. Writeyour answers below.

1. Before you play, make a conjecture. Do you think that each player has anequal chance of winning? Explain.

2. Now, play the game. Who won? What was the final score?

Read the Lesson3. How does a tree diagram resemble a tree?

4. How can you use a table to find the number of possible outcomes of anevent?

5. How do you know the game played in Example 3 is fair?

Remember What You Learned6. Draw a tree diagram that shows a fair game that is different from

the examples in your textbook. Can you think of a way to draw a tree diagram that shows a game that is not fair? Make sure you include a description if the game is not clear from your diagram.

6SDAP3.1

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionSample Spaces


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-2

WATCHES A certain type of watch comes in brown or black and in asmall or large size. Find the number of color-size combinations thatare possible.

Make a table to show the sample space. Then give the total number of outcomes.

There are four different color and size combinations.

CHILDREN The chance of having either a boy or a girl is 50%. What is the probability of the Smiths having two girls?

Make a tree diagram to show the sample space. Then find the probability of having two girls.

The sample space contains 4 possible outcomes. Only 1 outcome has both children beinggirls. So, the probability of having two girls is �

14�.

For each situation, make a tree diagram or table to show the samplespace. Then give the total number of outcomes.

1. choosing an outfit from a green shirt, blue shirt, or a red shirt, and blackpants or blue pants

2. choosing a vowel from the word COUNTING and a consonant from theword PRIME

boyboy

girl boy, girl

Child 1 Child 2 Sample Space

girlboy

girl

girl, boy

boy, boy

girl, girl

A game in which players of equal skill have an equal chance of winning is a fair game. A tree diagram or table is used to show all of the possible outcomes, or sample space, in a probabilityexperiment.

Color Size

Brown Small

Brown Large

Black Small

Black Large

Example 1

Example 2

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeSample Spaces


Less

on

9–2

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-2

The spinner at the right is spun twice.

1. Draw a tree diagram to represent the situation.

2. What is the probability of getting at least one A?

For each situation, make a tree diagram or table to show thesample space. Then give the total number of outcomes.

3. choosing a hamburger or hot dog and potato salad or macaronisalad

4. choosing a vowel from the word COMPUTER and a consonant from the word BOOK

5. choosing between the numbers 1, 2 or 3, and the colors blue, red, or green

B

C A

6SDAP3.1

For each situation, find the sample space using a table or treediagram.

1. choosing blue, green, or yellow wall paint with white, beige, or graycurtains

2. choosing a lunch consisting of a soup,salad, and sandwich from the menu shown in the table.

3. GAME Kimiko and Miko are playing a game in which each girl rolls anumber cube. If the sum of the numbers is a prime number, then Mikowins. Otherwise Kimiko wins. Find the sample space. Then determinewhether the game is fair.

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeSample Spaces


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-2

Soup Salad SandwichTortellini Caesar Roast Beef

Lentil Macaroni HamTurkey

blue

blue paint, white curtains

blue paint, beige curtains

blue paint, gray curtains

white

beige

gray

green paint, white curtains

green paint, beige curtains

green paint, gray curtains

white

beige

gray

yellow paint, white curtains

yellow paint, beige curtains

yellow paint, gray curtains

white

beige

gray

green

yellow

Paint Sample SpaceCurtains

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem Practice Sample Spaces


Less

on

9–2

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-2

1. GASOLINE Craig stops at a gas stationto fill his gas tank. He must choosebetween full-service or self-service andbetween regular, midgrade, andpremium gasoline. Draw a treediagram or table showing the possiblecombinations of service and gasolinetype. How many possible combinationsare there?

3. COINS In Exercise 2, what is theprobability of getting 2 heads, then 2 tails?

4. EQUIPMENT The computer accessorythat Joanne is considering selling ather store comes in white, beige, gray,or black and as an optical mouse,mechanical mouse, or trackball. Howmany combinations of color and modelmust she stock in order to have at leastone of every possible combination?

2. COINS Judy tosses a coin 4 times. Drawa tree diagram or table showing thepossible outcomes. What is theprobability of getting at least 2 tails?

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-2

Probabilities and RegionsThe spinner at the right can be used to indicate that the probability of landing in either of two regions is �

12�.

P(A) � �12� P(B) � �

12�

Read the description of each spinner. Using a protractor and ruler,divide each spinner into regions that show the indicated probability.

1. Two regions A and B: the probability of landing in region A is �34�.

What is the probability of landing in region B?

2. Three regions A, B, and C: the probability of landing in region A

is �12� and the probability of landing in region B is �

14�. What is the

probability of landing in region C?

3. Three regions A, B, and C: the probability of landing in region A

is �38� and the probability of landing in region B is �

18�. What is the

probability of landing in region C?

4. Four regions A, B, C, and D: the probability of landing in region A

is �116�

, the probability of landing in region B is �18�, and the probability

of landing in region C is �14�. What is the probability of landing in

region D?

5. The spinner at the right is an equilateral triangle, divided into regions by line segments that divide the sides in half. Is the spinner divided into regions of equal probability?

A

B

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____


Less

on

9–3

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-3


1. According to the table, how many sizes of juniors’ jeans are there?

2. How many lengths are there?

3. Find the product of the two numbers you found in Exercises 1 and 2.

4. Draw a tree diagram to help you find the number of different size and length combinations. How does the number of outcomes compare to the product you found above?

Read the Lesson5. What operation is used in the Fundamental

Counting Principle?

6. How is the information in a tree diagram or table different from the information provided by counting?

Remember What You Learned7. Write the Fundamental Counting Principle in your own words.

6SDAP3.1Lesson Reading GuideThe Fundamental Counting Principle

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-3

CLOTHING Andy has 5 shirts, 3 pairs of pants, and 6 pairs of socks.How many different outfits can Andy choose with a shirt, pair ofpants, and pair of socks?

Andy can choose 90 different outfits.

Use the Fundamental Counting Principle to find the total number ofoutcomes in each situation.

1. rolling two number cubes

2. tossing 3 coins

3. picking one consonant and one vowel

4. choosing one of 3 processor speeds, 2 sizes of memory, and 4 sizes of hard drive

5. choosing a 4-, 6-, or 8-cylinder engine and 2- or 4-wheel drive

6. rolling 2 number cubes and tossing 2 coins

7. choosing a color from 4 colors and a number from 4 to 10

If event M can occur in m ways and is followed by event N that can occur in n ways, then the event Mfollowed by N can occur in m � n ways. This is called the Fundamental Counting Principle.

number of shirts number of pants number of socks total number of outfits� � � �

5 � 3 � 6 � 90

Example 1

6SDAP3.1Study Guide and InterventionThe Fundamental Counting Principle

NAME ________________________________________ DATE ______________ PERIOD _____


Less

on

9–3

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-3


1. rolling two number cubes and tossing one coin

2. choosing rye or Bermuda grass and 3 different mixtures of fertilizer

3. making a sandwich with ham, turkey, or roast beef; Swiss or provolonecheese; and mustard or mayonaise

4. tossing 4 coins

5. choosing from 3 sizes of distilled, filtered, or spring water

6. choosing from 3 flavors of juice and 3 sizes

7. choosing from 35 flavors of ice cream; one, two, or three scoops; and sugaror waffle cone

8. picking a day of the week and a date in the month of April

9. rolling 3 number cubes and tossing 2 coins

10. choosing a 4-letter password using only vowels

11. choosing a bicycle with or without shock absorbers; with or withoutlights; and 5 color choices

12. a license plate that has 3 numbers from 0 to 9 and 2 letters

6SDAP3.1Skills Practice The Fundamental Counting Principle


1. choosing from 8 car models, 5 exterior paint colors, and 2 interior colors

2. selecting a year in the last decade and a month of the year

3. picking from 3 theme parks and 1-day, 2-day, 3-day, and 5-day passes

4. choosing a meat and cheese sandwich from the list shown in the table

5. tossing a coin and rolling 2 number cubes

6. selecting coffee in regular or decaf, with or without cream, and with orwithout sweeteners

7 COINS Find the number of possible outcomes if 2 quarters, 4 dimes, and 1nickel are tossed.

8. SOCIAL SECURITY Find the number of possible 9-digit social securitynumbers if the digits may be repeated.

9. AIRPORTS Jolon will be staying with his grandparents for a week. Thereare four flights that leave the airport near Jolon's home that connect toan airport that has two different flights to his grandparents’ hometown.Find the number of possible flights. Then find the probability of takingthe earliest flight from each airport if the flight is selected at random.

10. ANALYZE TABLES The table shows the kinds of homes offered by a residential builder. If the builder offers a discount on one home at random, find the probability it will be a 4-bedroom home with an open porch. Explain your reasoning.

NAME ________________________________________ DATE ______________ PERIOD _____


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-3

Number of Style of Type ofBedrooms Kitchen Porch5-bedroom Mediterranean Open4-bedroom Contemporary Screen3-bedroom Southwestern

Colonial

Cheese MeatProvolone SalamiSwiss TurkeyAmerican TunaCheddar Ham

6SDAP3.1PracticeThe Fundamental Counting Principle

NAME ________________________________________ DATE ______________ PERIOD _____


Less

on

9–3

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-3

1. SURFBOARD Jay owns 3 surfboards and2 wetsuits. If he takes one surfboardand one wetsuit to the beach, howmany different combinations can hechoose?

2. SHOPPING John is trying to decidewhich bag of dog food to buy. The brandhe wants comes in 4 flavors and 3 sizes.How many choices are there?

3. LOTTERY To purchase a lottery ticket,you must select 4 numbers from 0 to 9.How many possible lottery tickets canbe chosen?

4. RESTAURANTS Miriam’s favoriterestaurant has 3 specials every day.Each special has 2 choices of vegetableand 3 choices of dessert. How manydifferent meals could Miriam have?

5. ROUTES When Sunil goes to thebuilding where he works, he can gothrough 4 different doors into the lobby.Then he can go to the seventh floor bytaking 2 different elevators or 2different stairways. How manydifferent ways can Sunil get fromoutside the building to the seventhfloor?

6. STEREOS Jailin went to her local stereostore. Given her budget and theavailable selection, she can choosebetween 2 CD players, 5 amplifiers,and 3 pairs of speakers. How manydifferent stereos can Jailin purchase?

7. DESSERT For dessert you can chooseapple, cherry, blueberry, or peach pie toeat, and milk or juice to drink. Howmany different combinations can youchoose from?

8. TESTS John is taking a true or falsequiz. There are six questions on thequiz. How many ways can the quiz beanswered?

6SDAP3.1Word Problem PracticeThe Fundamental Counting Principle

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-3

Curious CubesIf a six-faced cube is rolled any number of times, the theoretical probability ofthe cube landing on any given face is �

16�.

Each cube below has six faces and has been rolled 100 times. Theoutcomes have been tallied and recorded in a frequency table. Basedon the data in each frequency table, what can you say are probablyon the unseen faces of each cube?

1.

2.

3.

4.

5.

14

5

14

5

Blue Red

Red

Yellow Blue

Red

14

5 Outcome Tally1 152 143 184 165 196 18

Outcome Tallyblue 17

red 30

yellow 53

Outcome Tallyred 30

blue 16

blank 54

Outcome Tally

1 34

4 32

5 34

Outcome Tally1 145 134 182 16

blank 39

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuidePermutations


Less

on

9–4

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-4


1. When you first started to make your list, how many choices did you havefor your first class?

2. Once your first class was selected, how many choices did you have for thesecond class? Then, the third class?

Read the Lesson3. Explain why the arrangement Science, Math, Language Arts is a

permutation of Math, Science, Language Arts.

4. In Example 1 on page 475, why is there only 1 choice for the third class?

5. In Example 2 on page 476, why are there only 7 choices for second place?

Remember What You Learned6. Look up the word permute in a dictionary. How does the meaning of this

word relate to the concepts in this lesson, especially the concept ofpermutations?

6SDAP3.1

Exercises

Example 2

Example 3

Example 1

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionPermutations


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-4

Find the value of 5 � 4 � 3 � 2 � 1.

5 � 4 � 3 � 2 � 1� 120 Simplify.

Find the value of 4 � 3 � 2 � 1 � 2 � 1.

4 � 3 � 2 � 1 � 2 � 1� 48 Simplify.

BOOKS How many ways can 4 different books be arranged on abookshelf?

This is a permutation. Suppose the books are placed on the shelf from left to right.There are 4 choices for the first book.

There are 3 choices that remain for the second book.There are 2 choices that remain for the third book.

There is 1 choice that remains for the fourth book.

4 � 3 � 2 � 1� 24 Simplify.

So, there are 24 ways to arrange 4 different books on a bookshelf.

Find the value of each expression.

1. 3 · 2 · 1 2. 7 · 6 · 5 · 4 · 3 · 2 · 1

3. 6 · 5 · 4 · 3 · 2 · 1 · 3 · 2 · 1 4. 9 · 8 · 7

5. How many ways can you arrange the letters in the word GROUP?

6. How many different 4-digit numbers can be created if no digit can berepeated? Remember, a number cannot begin with 0.

A permutation is an arrangement, or listing, of objects in which order is important. You can use theFundamental Counting Principle to find the number of possible arrangements.

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticePermutations


Less

on

9–4

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-4


1. 2 · 1 2. 4 · 3 · 2 · 1

3. 3 · 2 · 1 · 5 · 4 · 3 · 2 · 1 4. 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1

5. 2 · 1 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 6. 3 · 2 · 1 · 2 · 1

7. 11 · 10 · 9 8. 10 · 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1

9. 5 · 4 · 3 · 2 · 1 · 2 · 1 10. 5 · 4 · 3 · 2

11. 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 12. 6 · 5 · 4 · 3 · 2 · 1

13. How many ways can you arrange the letters in the word PRIME?

14. How many ways can you arrange 8 different crates on a shelf if they areplaced from left to right?

6SDAP3.1

Solve each problem.

1. NUMBERS How many different 2-digit numbers can be formed from thedigits 4, 6, and 8? Assume no number can be used more than once.

2. LETTERS How many permutations are possible of the letters in the wordNUMBERS?

3. PASSENGERS There are 5 passengers in a car. In how many ways can thepassengers sit in the 5 passenger seats of the car?

4. PAINTINGS Mr. Bernstein owns 14 paintings, but has only enough wallspace in his home to display three of them at any one time: one in thehallway, one in the den, and one in the parlor. How many ways can Mr.Bernstein display three paintings in his home?

5. DOG SHOW Mateo is one of the six dog owners in the terrier category. Ifthe owners are selected in a random order to show their dogs, how manyways can the owners show their dogs?

6. TIME Michel, Jonathan, and two of their friends each ride their bikes to school. If they have an equally-likely chance of arriving first, what isthe probability that Jonathan will arrive first and Michel will arrivesecond?

7. BIRTHDAY Glen received 6 birthday cards. If he is equally likely to readthe cards in any order, what is the probability he reads the card from hisparents and the card from his sister before the other cards?

CODES For Exercises 8–10, use the following information. A bank giveseach new customer a 4-digit code number which allows the newcustomer to create their own password. The code number is assignedrandomly from the digits 1, 3, 5, and 7, and no digit is repeated.

8. What is the probability that the code number for a new customer willbegin or end with a 7?

9. What is the probability that the code number will not contain a 5?

10. What is the probability that the code number will start with 371?

NAME ________________________________________ DATE ______________ PERIOD _____

PracticePermutations


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-4 6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem PracticePermutations


Less

on

9–4

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-4

1. AREA CODES How many different 3-digit area codes can be created if nodigit can be repeated?

2. CARDS Jason is dealt five playingcards. In how many different orderscould Jason have been dealt the samehand?

3. PASSWORDS How many different 3-letter passwords are possible if noletter may be repeated?

4. RACING All 22 students in Amy’s classare going to run the 100-meter dash. Inhow many ways can the students finishin first, second, and third place?

5. LETTERS How many ways can youarrange the letters in the wordHISTORY?

6. PARKING The parking lot for a companyhas three parking spaces for compactcars. The company has 8 employeeswith compact cars. How many ways canthe compact parking spaces be filled?

7. SERIAL NUMBERS How many different 6-digit serial numbers are available ifno digit can be repeated?

8. WINNERS There are 156 ways for 2 carsto win first and second place in a race.How many cars are in the race?

6SDAP3.1

Cyclic Permutations1. George, Alan, and William are in the same math class. George has five

different shirts and wears a different one each day. In how many wayscan George wear his five shirts in five days?

2. Alan has three different shirts and William has four. Which of the threestudents, George, Alan, or William, goes the greatest number of daysbefore he has to wear a shirt for the second time? Explain.

George, Alan, and William always wear their shirts in the same order.Suppose that George’s 5 shirts are red, tan, green, black, and white. He wears his shirts following this pattern:

B W R T G B W R T …

No matter where George is in the pattern, his friends can always figure outwhich shirt George will wear next. Since these permutations are the samewhen they make up part of a cycle, they are called cyclic permutations.

3. Alan has shirts that are white, black, and purple. Make an organized listof all the different permutations.

4. How many different ways are there for Alan to wear his shirts so that hisfriends recognize different patterns? Explain.

5. William has athletic shirts that are labeled 1, 2, 3, and 4. Make anorganized list of all the different permutations.

6. How many different ways are there for William to wear his shirts so that hisfriends recognize different patterns? Explain.

7. CHALLENGE For any given number of shirts, how can you determine thenumber of ways a person could wear the shirts to produce uniquepatterns?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-4 6SDAP3.1

Exercises

Example 1

NAME ________________________________________ DATE ______________ PERIOD _____

TI-83/84 Plus ActivityPermutations


Less

on

9–4

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-4

You can use a graphing calculator to help you find the number of permutations.

25 people are auditioning for 5 different parts in a play. In how many ways can the 5 parts be assigned?

To calculate a permutation, find the total number ofobjects (n) and the number taken at one time (r). In thisproblem, n � 25. Because 5 students are needed, r � 5.

Enter: 25 2 5 6,375,600

The parts can be assigned in 6,375,600 different ways.

Find the value of each permutation for the given values of n and r.

1. n � 5, r � 2 2. n � 8, r � 3 3. n � 9, r � 6

4. n � 6, r � 2 5. n � 10, r � 6 6. n � 12, r � 4

7. n � 20, r � 2 8. n � 15, r � 7 9. n � 18, r � 3

Solve.

10. Employees of Spies, Inc., are given 3-digit code numbers made up ofthe digits 1, 3, 5, 7, and 9. How many different 3-digit code numberscan be created?

11. How many different 4-letter arrangements are there in the letters A, S,N, D, T, R, and Y?

12. Twenty students have entered an art contest. Five students will eachreceive different awards. How many different groups of 5 studentscould be selected to receive awards?

ENTERMATH

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideCombinations


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-5


1. Use the first letter of each name to list all of the permutations of co-captains. How many are there?

2. Cross out any arrangement that contains the same letters as another onein the list. How many are there now?

3. Explain the difference between the two lists above.

Read the Lesson4. How can you find the number of combinations of objects in a set?

5. Why might it be easier to calculate the number of combinations of a set ofobjects using a permutation rather than making a list?

For Exercises 6 and 7, refer to Example 2 on page 525 in your textbook.

6. In the diagram, how many points are there? How many line segmentsconnect to any one point?

7. How does your answer to Exercise 6 above correspond to Example 2 inyour book?

Remember What You Learned8. Work with a partner. Take turns thinking of situations in which a

selection from a group must be made, where order is or is not important.Tell each other which situations are permutations and which arecombinations. Solve each problem and show your work.

6SDAP3.1

Exercises

Jill was asked by her teacher to choose 3 topics from the 8 topics given to her. How many different three-topic groups could she choose?

There are 8 · 7 · 6 permutations of three-topic groups chosen from eight. There are 3 · 2 · 1ways to arrange the groups.

�8 �7 � 6

� � �3366

� � 56

So, there are 56 different three-topic groups.

Tell whether each situation represents a permutation or combination.Then solve the problem.

On a quiz, you are allowed to answer any 4 out of the 6 questions.How many ways can you choose the questions?

This is a combination because the order of the 4 questions is not important. So, there are 6 · 5 · 4 · 3 permutations of four questions chosen from six. There are 4 · 3 · 2 · 1 orders inwhich these questions can be chosen.

�6 � 5

4�!4 � 3� � �

32640

� � 15

So, there are 15 ways to choose the questions.

Five different cars enter a parking lot with only 3 empty spaces.How many ways can these spaces be filled?

This is a permutation because each arrangement of the same 3 cars counts as a distinctarrrangement. So, there are 5 · 4 · 3 or 60 ways the spaces can be filled.


1. How many ways can 4 people be chosen from a group of 11?

2. How many ways can 3 people sit in 4 chairs?

3. How many ways can 2 goldfish be chosen from a tank containing 15 goldfish?

Example 2

Example 3

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionCombinations


Less

on

9–5

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-5

An arrangement, or listing, of objects in which order is not important is called a combination. You canfind the number of combinations of objects by dividing the number of permutations of the entire set bythe number of ways each smaller set can be arranged.

Example 1

6SDAP3.1

3 � 2 � 1

4 � 3 � 2 � 1

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeCombinations


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-5


1. You are allowed to omit two out of 12 questions on a quiz. How manyways can you select the questions to omit?

2. Six students are to be chosen from a class of 18 to represent the class at amath contest. How many ways can the six students be chosen?

3. How many different 5-digit zip codes are possible if no digits arerepeated?

4. In a race with six runners, how many ways can the runners finish first,second, or third?

5. How many ways can two names be chosen from 76 in a raffle if only oneentry per person is allowed?

6. How many ways can six students be arranged in a lunch line?

7. A family has a bike rack that fits seven bikes but they only have fivebikes. How many ways can the bikes fit in the bike rack?

8. How many ways can you select three sheriff deputies from eightcandidates?

9. How many ways can four finalists be selected from 50 contestants?

10. How many 4-digit pin numbers are available if no number is repeated?

11. How many handshakes can occur between five people if everyone shakeshands?

6SDAP3.1

Solve each problem.

1. BASKETBALL In how many ways can a coach select 5 players from a teamof 10 players?

2. BOOKS In how many ways can 3 books be selected from a shelf of 25books?

3. CAFETERIA In how many ways can you choose 2 side dishes from 15items?

4. CHORES Of 8 household chores, in how many ways can you do three-fourths of them?

5. ELDERLY Latanya volunteers to bake and deliver pastries to elderly peoplein her neighborhood. In how many different ways can Latanya deliver to2 of the 6 elderly people in her neighborhood?

6. DELI A deli makes potato, macaroni, three bean, Caesar, 7-layer, andGreek salads. The deli randomly makes only four salads each day. What isthe probability that the four salads made one day are 7-layer, macaroni,Greek, and potato?

7. AUTOGRAPHS A sports memorabilia enthusiast collected autographed baseballs from the players in the table. The enthusiast is giving one autographed baseball to each of his three grandchildren. If the baseballs are selected at random, what is the probability that the Hank Aaron, Alex Rodriquez,and Mickey Mantle autographed baseballs are given to his grandchildren?

For Exercises 8–10, tell whether each problem represents apermutation or a combination. Then solve the problem.

8. LOCKS In how many ways can three different numbers be selected from10 numbers to open a keypad lock?

9. MOVIES How many ways can 10 DVDs be placed on a shelf?

10. TRANSPORTATION Eight people need transportation to the concert. Howmany different groups of 6 people can ride with Mrs. Johnson?

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeCombinations


Less

on

9–5

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-5

PlayerCal RipkinHank AaronBarry BondsAlex RodriquezMickey Mantle

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem Practice Combinations


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-5

1. SNACKS A vending machine can displaysix snacks. If there are eight differentkinds of snacks available, how manydifferent groups of six different snackscan be displayed?

2. MUSIC Each month, Jose purchases twoCDs from a selection of 20 bestsellingCDs. How many different pairs of CDscan Jose choose if he chooses twodifferent CDs?

3. TESTS On a math test, you can chooseany 20 out of 23 questions. How manydifferent groups of 20 questions canyou choose?

4. RESTAURANTS The dinner special at alocal pizza parlor gives you the choiceof two toppings from a selection of sixtoppings. How many different choicesare possible if two different toppingsare chosen?

5. TESTING In a science fair experiment,two units are selected for testing fromevery 500 units produced. How manyways can these two units be selected?

6. MEETINGS Linda’s teacher divided theclass into groups of five and requiredeach member of a group to meet withevery other member of that group. Howmany meetings will each group have?

7. BASEBALL A baseball coach has 13players to fill nine positions. How manydifferent teams could he put together?

8. GEOMETRY Ten points are marked on acircle. How many different trianglescan be drawn between any threepoints?

6SDAP3.1

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Less

on

9–5

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-5

From Impossible to Certain EventsA probability is often expressed as a fraction. As you know, an event that isimpossible is given a probability of 0 and an event that is certain is given aprobability of 1. Events that are neither impossible nor certain are given aprobability somewhere between 0 and 1. The probability line below showsrelative probabilities.

Determine the probability of an event by considering its place on thediagram above.

1. Medical research will find a cure for all diseases.

2. There will be a personal computer in each home by the year 2010.

3. One day, people will live in space or under the sea.

4. Wildlife will disappear as Earth’s human population increases.

5. There will be a fifty-first state in the United States.

6. The sun will rise tomorrow morning.

7. Most electricity will be generated by nuclear power by the year 2010.

8. The fuel efficiency of automobiles will increase as the supply of gasolinedecreases.

9. Astronauts will land on Mars.

10. The percent of high school students who graduate and enter college willincrease.

11. Global warming problems will be solved.

12. All people in the United States will exercise regularly within the nearfuture.

equally likelyprettylikely

1

certainnot solikely

14

12

34

0

impossible

6SDAP3.1

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

TI-83/84 Plus ActivityCombinations


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-5

A graphing calculator can be used to solve problems involving combinations. On the TI-83/84Plus, the combination function can be found in the MATH (PRB) menu.

How many ways can 2 people be chosen from a group of 10 people?

Since order does not matter, this is a combination.

Enter: 10 3 2 45

So, the number of ways 2 people can be chosen from a group of 10 people is 45.

How many 5-card hands can be chosen from a deck of 52 cards?

Since order does not matter, this is a combination.

Enter: 52 3 5 2,598,960

So, the number of 5-card hands that can be chosen from a 52-card deck is2,598,960.

Solve each problem.

1. How many groups of 3 people can be chosen from a group of 5 people?





6. How many 2-topping pizzas can be made from a pizza restaurant offering 6 different toppings?

7. How many 3-topping pizzas can be made from a pizza restaurant offering 10 different toppings?

8. How many 7-card hands can be chosen from a deck of 52 cards?

9. How many 4-card hands can be chosen from a deck of 52 cards?

10. How many two-topping sundaes can be made from an ice cream shop offering 9 different toppings?

ENTERMATH

ENTERMATH

Example 1

Example 2

Exercises

Example

NAME ________________________________________ DATE ______________ PERIOD _____


Less

on

9–6

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-6

CLOTHING Ricardo has two shirts and three pairs of pants to chosefrom for his outfit to wear on the first day of school. How manydifferent outfits can he make by wearing one shirt and one pair ofpants?

By acting out a problem, you are able to see all possible solutions to the problem being posed.

Explore We know that he has two shirts and three pairs of pants to choose from. We canuse a coin for the shirts and an equally divided spinner labeled for the pants.

Plan Let’s make a list showing all possible outcomes of tossing a coin and thenspinning a spinner.

Solve H � HeadsT � TailsSpinner � 1, 2, 3

There are six possible outcomes of flipping a coin and spinning a spinner.So, there are 6 different possible outfits that Ricardo can wear for the first dayof school.

Check Flipping a coin has two outcomes and there are two shirts. Spinning a three-section spinner has three outcomes and there are three pairs of pants.Therefore, the solution of 6 different outcomes with a coin and spinnerrepresent the 6 possible outfit outcomes for Ricardo.

Flip a Coin Spin a SpinnerH 1H 2H 3T 1T 2T 3

1. SCIENCE FAIR There are 4 students with projects to present at the schoolscience fair. How many different ways can these 4 projects be displayedon four tables in a row?

2. GENDER Determine whether flipping a coin is a good way to predict thegender of the next 5 babies born at General Hospital. Justify youranswer.

3. OLYMPICS Four runners are entered in the first hurdles heat of twelveheats at the Olympics. The first two move on to the next round.Assuming no ties, how many different ways can the four runners come infirst and second place?

6SDAP3.2, 6SDAP2.4Study Guide and InterventionProblem-Solving Investigation: Act It Out

Use the act it out strategy to solve.

1. SCHOOL Determine whether rolling a 6-sided number cube is a good wayto answer a 20-question multiple-choice test if there are six choices foreach question. Justify your answer.

2. GYMNASTICS Five gymnasts are entered in a competition. Assuming thatthere are no ties, how many ways can first, second, and third places beawarded?

3. LUNCH How many ways can 3 friends sit together in three seats at lunch?

4. SCHEDULE How many different schedules can Sheila create if she has totake English, math, science, social studies, and art next semester. Assumethat there is only one lunch period available.

5. BAND CONCERTS The band is having a holiday concert. In the first row,the first trumpet is always furthest to the right and the first trombone isalways the furthest to the left. How many ways are there to arrange theother 4 people who need to sit in the front?

6. TEAMS Mr. D is picking teams for volleyball in gym by having thestudents count off by 2’s. The 1’s will be on one team and the 2’s on theother. Would flipping a coin would work just as well to pick the teams?Justify your answer.

NAME ________________________________________ DATE ______________ PERIOD _____


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-6 6SDAP3.2, 6SDAP2.4Skills PracticeProblem-Solving Investigation: Act it Out

Select the Operation

Mixed Problem Solving

For Exercises 1 and 2, use the act it outstrategy.

1. POP QUIZ Use the information in thetable to determine whether tossing anickel and a dime is a good way toanswer a 5-question multiple-choicequiz if each question has answer choicesA, B, C, and D. Justify your answer.

2. BOWLING Bill, Lucas, Carmen, andDena go bowling every week. Whenordered from highest to lowest, howmany ways can their scores be arrangedif Lucas is never first and Carmenalways beats Bill?

Use any strategy to solve Exercises 3and 4. Some strategies are shown below.

3. BOOKS What is the probability of fivebooks being placed in alphabetical orderof their titles if randomly put on a bookshelf?

4. NUMBER THEORY The sum of a 2-digitnumber and the 2-digit number whenthe digits are reversed is 77. If thedifference of the same two numbers is45, what are the two 2-digit numbers?

For Exercises 5 and 6, select theappropriate operation(s) to solve theproblems. Justify your solution(s) andsolve the problem.

5. BASEBALL In one game, Rafael was up tobat 3 times and made 2 hits. In anothergame, he was up to bat 5 times with nohits. What percent of the times at batdid Rafael make a hit?

6. RESTAURANT A restaurant offers thepossibility of 168 three-course dinners.Each dinner has an appetizer, an entrée,and a dessert. If the number ofappetizers decreases from 7 to 5, findhow many fewer possible three-coursedinners the restaurant offers.

NAME ________________________________________ DATE ______________ PERIOD _____


Less

on

9–6

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-6

PROBLEM-SOLVING STRATEGIES

• Use the four-step plan.

• Draw a diagram.

• Determine reasonable answers.

• Act it out.

Nickel Dime Answer ChoiceH H AH T BT H CT T D

6SDAP3.2, 6SDAP2.4PracticeProblem-Solving Investigation: Act It Out

Solve each problem using any strategy you have learned.

NAME ________________________________________ DATE ______________ PERIOD _____


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-6

3. BASEBALL Thirty-two teams are playingin the championship. If a team iseliminated once it loses, how manytotal games will be played in thechampionship?

4. GEOMETRY Find the next two terms inthe sequence.

5. POOL RENTAL The table below showshow much Ford Middle School wascharged to rent the pool for a partybased on the number of hours it wasrented. Predict the cost for 5 hours.

6. GEOMETRY Use the formula D � rtwhere D is the distance, r is the rate,and t is the time to determine how farAlyssa drove if she drove 55 miles perhour for 4 hours.

7. SCHOOL ELECTIONS How many ways can a president, vice president,secretary and treasurer be elected from a choice of 6 students?

8. SHOPPING Morty bought skis. The skiscost $215 and he got $35 in change.How much did Morty pay with?

# of hours Cost1 $1201.5 $1802 $2402.5 $300

1. POLLS Out of 200 people, 32% said thattheir favorite animal was a cat and44% said that their favorite animal wasa dog. How many more people chosedog than cat?

2. PEACHES Roi is picking peaches He

needs a total of 3�12

� bushels of peaches.

If he has already picked 3 bushels, howmany more does he need to pick?

A 2 bushels C 3�12

� bushels

B �12

� bushel D 3 bushels

6SDAP3.2, 6SDAP2.4Word Problem PracticeProblem-Solving Investigation: Act It Out


1. Compare the number of times you expected to roll a sum of 7 with thenumber of times you actually rolled a sum of 7. Then compare your resultto the results of other groups.

2. Write the probability of rolling a sum of 7 out of 36 rolls using thenumber of times you expected to roll a 7 from Step 1. Then write theprobability of rolling a sum of 7 out of 36 rolls using the number of timesyou actually rolled a sum of 7 from Step 2.

Read the Lesson3. Look up the word experimental in a dictionary. Write the meaning for the

word as used in the lesson.

4. How does theoretical probability differ from experimental probability?

5. Complete the sentence: Experimental probability can be based onand can be used to make predictions about future

events.

Remember What You Learned6. Work with a partner. Design an experiment that you can use to express

the experimental probability of an event. Compare your findings withthose of others in your class.

NAME ________________________________________ DATE ______________ PERIOD _____


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-7

Less

on

9–7

6SDAP3.2Lesson Reading Guide Theoretical and Experimental Probability

Exercises

The graph shows the results of an experiment in which a number

cube was rolled 100 times. Find the experimentalprobability of rolling a 3 for this experiment.

P(3) �

� �11060�

or �245�

The experimental probability of rolling a 3 is �245�

, which is close to its theoretical

probabilityof �16�.

In a telephone poll, 225 people were asked for whom they planned to vote in the race

for mayor. What is the experimental probability of Juarez being elected?

Of the 225 people polled, 75 planned to vote for Juarez.

So, the experimental probability is �27255�

or �13�.

Suppose 5,700 people vote in the election.How many can be expected to vote for Juarez?

�13� � 5,700 � 1,900

About 1,900 will vote for Juarez.

For Exercises 1–3, use the graph of a survey of 150 students asked whether they prefer cats or dogs.

1. What is the probability of a student preferring dogs?

2. Suppose 100 students were surveyed. How many can be expected to prefer dogs?

3. Suppose 300 students were surveyed. How many can be expected to prefer cats? DogsCats

60

80

100

40

0

20

120

140

Num

ber o

f Stu

dent

s

18

132

number of times 3 occurs��number of possible outcomes

6321

20

10

15

25

0

5Num

ber o

f Rol

ls

54

14 1316

1921

17

Number Showing

NAME ________________________________________ DATE ______________ PERIOD _____


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-7

Experimental probability is found using frequencies obtained in an experiment or game. Theoreticalprobability is the expected probability of an event occurring.

CandidateNumber of

PeopleJuarez 75Davis 67Abramson 83

Example 1

Example 2

Example 3

6SDAP3.2Study Guide and InterventionTheoretical and Experimental Probability

For Exercises 1–5, a number cube is rolled 50 times and the resultsare shown in the graph below.

1. Find the experimental probability of rolling a 2.

2. What is the theoretical probability of rolling a 2?

3. Find the experimental probability of not rolling a 2.

4. What is the theoretical probability of not rolling a 2?

5. Find the experimental probability of rolling a 1.

For Exercises 6–9, use the results of the survey at the right.

6. What is the probability that a person’s favorite season is fall? Write the probability as a fraction.

7. Out of 300 people, how many would you expect to say that fall is their favorite season?

8. Out of 20 people, how many would you expect to say that they like all theseasons?

9. Out of 650 people, how many more would you expect to say that they likesummer than say that they like winter?

Spring

Summer

Fall

Winter

None, I likethem all

13%

39%

25%

13%

10%

What is your favoriteseason of the year?

6321

8

10

12

4

6

14

0

2

Num

ber o

f Rol

ls

54

108

6

9

5

12

NAME ________________________________________ DATE ______________ PERIOD _____


Less

on

9–7

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-7 6SDAP3.2Skills Practice

Theoretical and Experimental Probability

For Exercises 1–4, a number cube is rolled 24 times and lands on 2four times and on 6 three times.

1. Find the experimental probability of landing on a 2.

2. Find the experimental probability of not landing on a 6.

3. Compare the experimental probability you found in Exercise 1 to itstheoretical probability.

4. Compare the experimental probability you found in Exercise 2 to itstheoretical probability.

ENTERTAINMENT For Exercises 5–7, use the results of the survey in the table shown.

5. What is the probability that someonein the survey considered readingbooks or surfing the Internet as thebest entertainment value? Write theprobability as a fraction.

6. Out of 500 people surveyed, how manywould you expect considered readingbooks or surfing the Internet as thebest entertainment value?

7. Out of 300 people surveyed, is itreasonable to expect that 30considered watching television as thebest entertainment value? Why or whynot?

For Exercises 8–10, a spinner marked with four sections blue, green,yellow, and red was spun 100 times. The results are shown in the table.

8. Find the experimental probability of landing on green.

9. Find the experimental probability of landing on red.

10. If the spinner is spun 50 more times,how many of these times would you expect the pointer to land on blue?

NAME ________________________________________ DATE ______________ PERIOD _____


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-7

Section FrequencyBlue 14

Green 10Yellow 8

Red 68

Best Entertainment ValueType of Entertainment PercentPlaying Interactive Games 48%Reading Books 22%Renting Movies 10%Going to Movie Theaters 10%Surfing the Internet 9%Watching Television 1%

6SDAP3.2PracticeTheoretical and Experimental Probability

NAME ________________________________________ DATE ______________ PERIOD _____


Less

on

9–7

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-7

HOBBIES For Exercises 1–3, use the WINTER ACTIVITIES For Exercises 5 and 6,graph of a survey of 24 seventh grade use the graph of a survey with 104students asked to name their favorite responses in which respondents were hobby . asked about their favorite winter

activities.

10 20 30 40 50 60 700

Building a snowmanSnowboarding/skiing

Sledding

What is your favorite winter activity?

1469

21

Respondents

2 4 6 8 10 12 140

SingingHanging with friends

Building thingsBike riding

T.V.Computer

Roller skatingSports

What is your favorite hobby?

13

12

333

8

Number of Students

1. What is the probability that a student’sfavorite hobby is roller skating?

2. Suppose 200 seventh grade studentswere surveyed. How many can beexpected to say that roller skating istheir favorite hobby?

3. Suppose 60 seventh grade studentswere surveyed. How many can beexpected to say that bike riding is theirfavorite hobby?

4. MARBLES A bag contains 5 blue, 4 red,9 white, and 6 green marbles. If amarble is drawn at random andreplaced 100 times, how many timeswould you expect to draw a greenmarble?

5. What is the probability that someone’sfavorite winter activity is building asnowman? Write the probability as afraction.

6. If 500 people had responded, how manywould have been expected to listsledding as their favorite winteractivity? Round to the nearest wholeperson.

6SDAP3.2Word Problem PracticeTheoretical and Experimental Probability

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-7

Rolling a DodecahedronA dodecahedron is a solid. It has twelve faces, and each face is a pentagon.

At the right, you see a dodecahedron whose faces are marked with the integers from 1 through 12. You can roll this dodecahedron just as you roll a number cube. With the dodecahedron, however, there are twelve equally likely outcomes.

Refer to the dodecahedron shown at the right. Find the probability of each event.

1. P(5) 2. P(odd)

3. P(prime) 4. P(divisible by 5)

5. P(less than 4) 6. P(fraction)

You can make your own dodecahedron by cutting out the pattern at the right. Fold along each of the solid lines. Then use tape to join the faces together so that your dodecahedron looks like the one shown above.

7. Roll your dodecahedron 100 times. Record your results on a separate sheet of paper, using a table like this.

8. Use your results from Exercise 7. Find the experimental probability for each of the events described in Exercises 1–6.

Outcome

1

2

Tally Frequency

1 2

3

45

6

7

11

128

9

10

2

11 10

1

36

6SDAP3.2

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

TI-73 ActivityExperimental Probability


Less

on

9–7

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-7

Use your calculator to simulate flipping a coin or rolling a number cube. These features arefound in the MATH PRB (probability) menu. The calculator displays a random number thatrepresents heads or tails on a coin or the number on a number cube. The calculator callsnumber cubes dice.

Roll two number cubes 100 times. Calculate the experimental probability ofrolling double-1, double-2, double-3, double-4, double-5, or double-6.

Step 1 Clear Home. Step 2 Choose the dice feature in MATH PRB.

[MEM] 5 7

Step 3 The display shows dice( . Use 2 dice. Step 4 Interpret the result and continue for

2 100 rolls.

The display shows an ordered pair of digits, like (3 5). This means the first cube shows a 3 and thesecond cube shows a 5. If a double, like (2 2) or (5 5), appears, tally it in the chart below. Continue with the next roll by pressing .

Use your graphing calculator to complete the following.

1. Complete the table for 100 rolls. Calculate the Fraction and Percentcolumns.

2. The theoretical probability ofrolling double-1 (or any otherdouble) is 1/36 or about 3%.Compare this theoreticalprobability with yourexperimental results.

3. Do another experiment, but use the coin feature of MATH PRB. Explore the probability of afamily with three children having all girls. Flip 3 coins. Each coin stands for one child. If theresult is a 1, then the child is a boy; if it is 0, then the child is a girl. Flip the three coins 100 times. Tally the results of 3 girls and of 3 boys. Describe your results.

ENTER

ENTER

MATHENTER2nd

Double Tally Number Fraction Percent

(1, 1)

(2, 2)

(3, 3)

(4, 4)

(5, 5)

(6, 6)

Tally Number Fraction Percent

All girls (0, 0, 0)

All boys (1, 1, 1)

Example 1

NAME ________________________________________ DATE ______________ PERIOD _____

Lesson Reading GuideCompound Events


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-8


1. What is the probability of Omar being in the second heat? in Lane 3?

2. Multiply your answers in Exercises 1. What does this number represent?

Read the LessonUse the introduction to the lesson to answer Exercises 4–6.

3. What does a compound event consist of?

4. Define independent events.

5. Write the probability of independent events in symbols.

6. How can you find the probability of two independent events?

Remember What You Learned7. List several independent compound events. Explain why you consider the

events to be independent.

6SDAP3.4, 6SDAP3.5

Exercises

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionCompound Events


Less

on

9–8

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-8

A coin is tossed and a number cube is rolled. Find the probabilityof tossing tails and rolling a 5.

P(tails) � �12� P(5) � �

16�

P(tails and 5) � �12� � �

16� or �1

12�

So, the probability of tossing tails and rolling a 5 is �112�

.

MARBLES A bag contains 7 blue, 3 green, and 3 red marbles. If Agnes randomly draws two marbles from the bag, replacing the first

before drawing the second, what is the probability of drawing a green and then ablue marble?

P(green) � 3/131 13 marbles, 3 are green

P(blue) � 7/13 13 marbles, 7 are blue

P(green, then blue) � �133�

· �172�

� �12619

�

So, the probability that Agnes will draw a green, then a blue marble is �12619

�.

1. Find the probability of rolling a 2 and then an even number on twoconsecutive rolls of a number cube.

2. A penny and a dime are tossed. What is the probability that the pennylands on heads and the dime lands on tails?

3. Lazlo’s sock drawer contains 8 blue and 5 black socks. If he randomlypulls out one sock, what is the probability that he picks a blue sock?

A compound event consists of two or more simple events. If the outcome of one event does not affectthe outcome of a second event, the events are called independent events. The probability of twoindependent events can be found by multiplying the probability of the first event by the probability ofthe second event.

Example 1

Example 2

6SDAP3.4, 6SDAP3.5

NAME ________________________________________ DATE ______________ PERIOD _____

Skills PracticeCompound Events


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-8

1. Four coins are tossed. What is the probability of tossing all heads?

2. One letter is randomly selected from the word PRIME and one letter israndomly selected from the word MATH. What is the probability thatboth letters selected are vowels?

3. A card is chosen at random from a deck of 52 cards. It is then replacedand a second card is chosen. What is the probability of getting a jack andthen an eight?

For Exercises 4–6, use the information below.

A standard deck of playing cards contains 52 cards in four suits of 13 cardseach. Two suits are red and two suits are black. Find each probability. Assumethe first card is replaced before the second card is drawn.

4. P(black, queen) 5. P(black, diamond) 6. P(jack, queen)

7. What is the probability of spinning a number greater than 5 on a spinnernumbered 1 to 8 and tossing a tail on a coin?

8. Two cards are chosen at random from a standard deck of cards withreplacement. What is the probability of getting 2 aces?

9. A CD rack has 8 classical CDs, 5 pop CDs, and 3 rock CDs. One CD ischosen and replaced, then a second CD is chosen. What is the probabilityof choosing a rock CD then a classical CD?

10. A jar holds 15 red pencils and 10 blue pencils. What is the probability ofdrawing one red pencil from the jar?

6SDAP3.4, 6SDAP3.5

A number cube is rolled and a spinner like the one shown is spun. Find each probability.

1. P(6 and D) 2. P(multiple of 2 and B) 3. P(not 6 and not A)

A set of 7 cards is labeled 1–7. A second set of 12 cards contains the followingcolors: 3 green, 6 red, 2 blue, and 1 white. One card from each set is selected. Findeach probability.

4. P(6 and green) 5. P(prime and blue) 6. P(odd and red)

7. P(7 and white) 8. P(multiple of 3 and red) 9. P(even and white)

A coin is tossed, a number cube is rolled, and a letter is picked fromthe word framer.

10. P(tails, 5, m) 11. P(heads, odd, r) 12. P(heads, 6, vowel)

13. P(tails, prime, consonant) 14. P(not tails, multiple of 3, a) 15. P(not heads, 2, f )

16. TOLL ROAD Mr. Espinoza randomly chooses one of five toll booths whenentering a toll road when driving to work. What is the probability he willselect the middle toll booth on Monday and Tuesday?

MARBLES For Exercises 17–20, use theinformation in the table shown to find eachprobability. After a marble is randomly pickedfrom a bag containing marbles of four differentcolors, the color of the marble is observed andthen it is returned to the bag.

17. P(red) 18. P(green, blue)

19. P(red, white, blue) 20. P(blue, blue, blue)

A

D

CB

NAME ________________________________________ DATE ______________ PERIOD _____

PracticeCompound Events


Less

on

9–8

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-8

MarblesColor NumberWhite 6Green 2Red 1Blue 3

6SDAP3.4, 6SDAP3.5

NAME ________________________________________ DATE ______________ PERIOD _____

Word Problem Practice Compound Events


Copyright ©

Glencoe\M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-8

1. SAFETY Eighty percent of all Californiadrivers wear seat belts. If three driversare pulled over, what is the probabilitythat all would be wearing their seatbelts? Write as a percent to the nearesttenth.

2. VEGETABLES A nationwide surveyshowed that 65% of all children in theUnited States dislike eating vegetables.If three children are chosen at random,what is the probability that all threedislike eating vegetables? Write as apercent to the nearest tenth.

3. QUALITY In a shipment of 50calculators, 4 are defective. Onecalculator is randomly selected andtested. What is the probability that it isdefective?

4. MARBLES A bag contains 6 greenmarbles, 2 blue marbles, and 3 whitemarbles. Gwen draws one marble fromthe jar and replaces it. Jeff then drawsone marble from the jar. What is theprobability that Gwen draws a bluemarble and Jeff draws a white marble?

5. DEMONSTRATION Ms. Morris needs astudent to help her with ademonstration for her class of 12 girlsand 14 boys. She randomly chooses astudent. What is the probability thatshe chooses a girl?

6. SURVEY Ruben surveyed his class andfound that 4 out of 22 students walk toschool. If one of the 22 students isselected at random, what is theprobability that the chosen studentDOES NOT walk to school?

6SDAP3.4, 6SDAP3.5

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Less

on

9–8

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9-8

Compound EventsThe game of roulette is played by dropping a ballinto a spinning, bowl-shaped wheel. When thewheel stops spinning, the ball will come to rest inany of 38 locations.

On a roulette wheel, the eighteen even numbersfrom 2 through 36 are colored red and theeighteen odd numbers from 1 through 35 arecolored black. The numbers 0 and 00 are coloredgreen.

To find the probability of two independent events,the results of two spins, find the probability ofeach event first.

P(red) � �1388�

or �199�

P(black) � �1388�

or �199�

Then multiply.

P(red, then black) � �199�

� �199�

or �38611�

Find each probability.

1. black, then black

2. prime number, then a composite number

3. a number containing at least one 0, then a number containing at leastone 2

4. red, then black

5. the numbers representing your age, month of birth, and then day of birth

0 3 9 15 20 3226

410

1621

3327

5

1117223428006122335

2918

713

124

3036

8

214 19 31 25

6SDAP3.4, 6SDAP3.5

NAME ________________________________________ DATE ______________ PERIOD _____

TI-73 ActivityProbability and Percents


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

9-8

When you solve probability problems, use your calculator to express fractions as decimalsand percents.

Two number cubes are rolled. Find the probability that both cubes show anodd number. Report the probability as a percent.

The probability of a cube showing an odd number is �12�. To find the probabilitythat both first and second cubes are odd, multiply �12� by �12�.

Keys: 1 2 1 2 Display: �21� * �2

1� �4

1�

�41� .25

100 Ans*100 25

The probability that both cubes show odd numbers is 25%.

There are 3 red marbles and 5 blue marbles in a bag. Two marbles are drawnand the first marble is replaced before the second is drawn.What is theprobability of drawing 2 blue marbles? Report the probability as a percent.

Keys: Display:

5 8 5 8 �85

�*�85

� �625

4�

Display: �625

4� 0.390625100 Display:Ans*100 0.390625

The probability of drawing 2 blue marbles is 39.06%.

Find each probability. Report your answer as a percent. Round percents to thenearest hundredth when necessary.

1. You draw 2 marbles from a bag replacing the first marble before drawing the second. The bagcontains 4 yellow marbles, 2 white marbles, and 6 red marbles.

a. What is the probability that your first marble is red and the second is yellow?

b. What is the probability that both marbles are white?

c. What is the probability that neither marble is red?

d. What is the probability that both marbles are red?

2. You have three number cubes.

a. What is the probability that you will roll all even numbers?

b. What is the probability that you will roll only numbers less than 3?

c. CHALLENGE What is the probability that you will roll a 1 on only one number cube?

ENTER

ENTERF D

ENTERbcbc

ENTER

ENTERF D

ENTERbcbc

F D←←

F D←←

Example 1

Example 2

NAME ________________________________________ DATE ______________ PERIOD _____

Student Recording SheetUse this recording sheet with pages 504–505 of the Student Edition.


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.9

Read each question. Then fill in thecorrect answer.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Record your answers for Question 12 onthe back of this paper.

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

Pre-AP

Ass

essm

ent

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


9 Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 505 of the Student Edition.)

General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she

arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.

Exercise 12 Rubric

Score Specific Criteria4 A correct tree diagram is given. The propability that Paula will hear a country song

first on Friday night is correctly determined to be �15

�. The probability that Paula

will hear a rap song first on Friday night and a jazz song first on Saturday night is

correctly determined to be �15

�. �15

� or �215�

3 The probabilities are computed correctly, but there are one or two mistakes in thetree diagram.

2 The probabilities are computed correctly, but the tree diagram is incorrect or notgiven. ORThe tree diagram is correct, but only one of the probabilities is computed correctly.

1 The tree diagram is correct, but neither probability is computed correctly. OROne probability is computed correctly, but the other probability and the treediagram are incorrect or not given.

0 Response is completely incorrect.

For Questions 1–3, a bag contains 3 blue, 5 red, and 8 yellow balls. Find each probability if you draw one ball at random from the bag. Write as a fraction insimplest form.

1. P(yellow)

2. P(blue or red)

3. P(not blue)

4. Make a tree diagram on another piece of paper to find the number of ways you can arrange the colors yellow, red, blue,and green if no color can be used more than once. What is the total number of possible arrangements?

5. MULTIPLE CHOICE Supose there are 2 colors (red and blue) for 4 cars (one color per car). Give the total number of possible car-color choices.

A. 4 choices B. 6 choices C. 8 choices D. 10 choices

1.

2.

3.

4.

5.

1. There are 3 paths connecting the library and the post office,2 paths connecting the post office and the bank, and 4 pathsconnecting the bank to home. Find the number of ways towalk from the library to home.

2. SNEAKERS An athletic shoe manufacturer makes sneakers that are white leather or one of three canvas colors with lace-up or Velcro closures. How many different sneakers can be made?

3. In how many ways can a president and vice-president berandomly selected from a class of 28 students?

4. How many permutations are possible of the letters in the word plant?

5. In how many ways can 8 pieces of luggage be arranged on a conveyor belt?

1.

2.

3.

4.

5.


Chapter 9 Quiz 1(Lessons 9-1 and 9-2)


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

9

9

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. ART How many ways can 4 Van Gogh and 5 Monet paintings be hung in 4 spaces if order is not important?

2. CARROTS Austin has 10 carrots and he wants to feed 6 of them to his rabbits. How many ways can he do this?

3. In how many ways can you pick 3 fish from a tank of 9 iforder is not important?

4. Five people are getting into a car. Two people have already claimed the front seats. In how many different ways can the back three seats be taken?

5. There are six finalists in the science fair. In how many different ways can first and second places be awarded?

1.

2.

3.

4.

5.

SHIRTS Grant has 6 different shirts to choose from: maroon,blue, brown, gold, green, and purple.

1. If Grant selects a shirt at random, what is the probability it will be blue or green?

2. If Grant chooses shirts 10 times and chooses the gold one 4 times, what is the experimental probability that the gold shirt is chosen?

3. Find the theoretical probability that a gold shirt is chosen.Discuss any difference between this result and the result found in Question 2.

4. A coin is tossed, and a number cube is rolled. Find P(tails, factor of 12).

5. Four rap CDs, seven dance CDs, two country CDs,three R & B CDs, and five pop CDs are on a shelf.Without replacing the first CD, Ryan takes a second.Find P(R & B, then dance).

1.

2.

3.

4.

5.




NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

9

9

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Write the letter for the correct answer in the blank at the right of each question.

Use the spinner at the right to find each probability. Write as a fraction in simplest form.

1. P(C)

A. �18� B. �

16

� C. �13�� D. 6

2. P(vowel)

F. �16� G. �

13

� H. �12� J. 3

3. P(not D)

A. 5 B. �56� C. �

58� D. �

16�

4. LETTERS How many permutations are possible of the letters in the word locker?

F. 720 G. 120 H. 21 J. 6

5. ART Eight different color markers are in a box: red, blue, green,yellow, pink, purple, brown, and black. Anne randomly selects two.What is the probability that she selects a red and blue marker?

A. �614� B. �

516� C. �

14

� D. �18

�

6. CONCERT There are four soloists at an orchestra concert. In how many different orders can the musicians play a solo during the evening?F. 4 G. 10 H. 12 J. 24

For each situation, use a tree diagram to find the total number of outcomes.7. tossing a quarter and tossing a penny

8. choosing to watch TV or read a book and choosing pretzels,an apple, or popcorn for a snack

9. choosing a book to read from 5 mysteries and choosing another book to read from 6 biographies

Use the Fundamental Counting Principle to find the total number of outcomes in each situation.10. choosing belt buckles from a collection of 6 bronze,

4 wooden, and 5 silver belt buckles if you choose one of each kind of buckle

11. choosing a school sweatshirt that is gray or white and choosing small, medium, large, or extra-large

12. choosing toast, muffin, or bagel and choosing coffee, milk,or juice

13. choosing an album, CD, and cassette to listen to from a collection of 5 albums, 7 CDs, and 4 cassettes

A

E

F

C

B

D

7.

8.

9.

10.

11.

12.

13.

1.

2.

3.

4.

5.

6.

Chapter 9 Mid-Chapter Test(Lessons 9-1 and 9-4)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____9


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


9 Chapter 9 Vocabulary Test

Choose from the terms above to complete each sentence.

1. A(n) _______________ is a possible result.

2. Probability found using frequencies in a game or experimentis called _______________.

3. A(n) _______________ is not affected by the outcome of theprevious event.

4. The set of all possible outcomes is called the _______________.

5. A(n) _______________ is one of two events that are the onlyones that can possibly happen and the sum of whose probabilities is 1.

6. A(n) _______________ is an arrangement, or listing, of objectsin which order is important.

7. The chance of an event happening is called _______________.

8. A(n) _______________ is an arrangement, or listing, in which order is not important.

9. In a _______________, all players of equal skill have an equal chance of winning.

10. A(n) _______________ is made up of two or more simple events.

Define the term in your own words.

11. Fundamental Counting Principle

combination complementary events compound events experimental probability fair game Fundamental Counting Principle independent events outcome

permutation probability random sample space simple event theoretical probability tree diagram

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


1. How many different 4-digit numbers are there if no digit is repeated?A. 4 B. 24 C. 504 D. 4,536

2. In how many ways can you choose 2 side dishes out of 8?F. 56 G. 28 H. 16 J. 4

DOGS The boarders at a kennel are made up of the following dogs. If one dog is randomly selected for a 30-minute training session, find theprobability of each event. The fractions are written in simplest form.

3. P(retriever)

A. �34� B. �

35� C. �

12� D. �

38�

4. P(not male)

F. �1294�

G. �172�

H. �12� J. �2

74�

5. P(cat)

A. 0 B. �1100�

C. �12� D. 1

For Questions 6–8, use the Fundamental Counting Principle to find thetotal number of outcomes in each situation.

6. tossing a quarter and a pennyF. 1 G. 2 H. 4 J. 8

7. choosing a meat, a vegetable, and a beverage from 3 kinds of meat, 2 kinds of vegetables, and 4 kinds of beveragesA. 9 B. 10 C. 24 D. 48

8. picking a day of the week and rolling a number cubeF. 13 G. 14 H. 30 J. 42

9. A blue number cube and an orange number cube are rolled.Find P(3, then even).

A. �65� B. �

23� C. �

16� D. �1

12�

10. A bag contains 3 orange, 5 black, and 2 white marbles. Two marbles aredrawn, but the first marble is not replaced. Find P(white, then black).

F. �59� G. �

19� H. �1

10�

J. �115�

Use a tree diagram.

11. TESTS Justine is taking a test with four true/false questions. How many possible ways can the four answers appear on the test? A. 4 B. 8 C. 16 D. 32

12. RINGS Lianna has enough money to buy one ring. She can choose a silver or a gold band and an onyx, opal, or topaz setting. From how many different combinations does she have to choose?F. 2 G. 4 H. 6 J. 8

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 9 Test, Form 1C

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.

BoardersMales 10Females 14Pointers 6Retrievers 18

Tell whether each problem represents a permutation (P) or a combination (C). Then solve the problem.

13. Ten students remain in a game of musical chairs. If four chairs are removed, how many different groups of six students can remain?A. P; 65 B. C; 105 C. C; 210 D. C; 420

14. How many different ways can five airplanes be arranged at five gates?F. C; 5 G. C; 24 H. P; 96 J. P; 120

15. In how many ways can Zoe choose 4 figurines from a collection of 7?A. C; 11 B. C; 28 C. C; 35 D. P; 5,040

16. RACING In a cross-country race with 8 runners, how many different ways can they come across the finish line?F. P; 40,320 G. P; 5,760 H. C; 1,120 J. C; 36

BASEBALL Corey has two tickets to a baseball game. He can take one of hisfriends with him, but five of his friends would like to go. They are Jane,Meg, Matt, Ted, and Amy. To decide, Corey writes each of his friends’names on a separate piece of paper and selects one.

17. What is the probability that Corey picks a boy?

A. �15� B. �

25� C. �

35� D. �

23�

18. What is the probability that Corey picks someone whose name does not beginwith the letter M?

F. �35� G. �

25� H. �

15� J. �

16�

19. If Corey draws a name 20 times and Amy’s name is picked twice, what is theexperimental probability that Amy’s name is picked?

A. �25� B. �

15� C. �

16� D. �1

10�

20. Choose the best comparison between the theoretical and experimentalprobability that Amy will go to the game. Use the experimental probabilityfrom Question 19.F. The theoretical probability is greater than the experimental probability.G. The theoretical probability is less than the experimental probability.H. The theoretical probability is equal to the experimental probability.J. The theoretical probability is not related to the experimental probability.

Bonus CLASSES Tim can select 4 of his classes from the following options: algebra, American Sign Language, typing, English,Spanish, tennis, and science. What is the probability that Tim will select science, algebra, typing, and Spanish?

13.

14.

15.

16.

17.

18.

19.

20.

B:

NAME ________________________________________ DATE ______________ PERIOD _____


9 Chapter 9 Test, Form 1 (continued)C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.


1. How many different 5-digit numbers are there if no digit is repeated?A. 120 B. 720 C. 15,120 D. 27,216


DOGS The boarders at a kennel are made up of the following dogs. If one dog is randomly selected for a 30-minute training session, find the probability of each event. The fractions are written in simplest form.

3. P(female)

A. �172�

B. �12� C. �1

77�

D. �274�

4. P(not pointer)

F. �38� G. �

12� H. �

34� J. �

78�

5. P(pointer or retriever)

A. 24 B. 1 C. �12� D. 0

For Questions 6–8, use the Fundamental Counting Principle to find the total number of outcomes in each situation.

6. tossing a nickel, a quarter, a penny, and rolling a number cubeF. 4 G. 12 H. 24 J. 48

7. choosing coffee or tea, with cream, milk, or honey served in a glass or a plastic cupA. 24 B. 12 C. 7 D. 6

8. picking a number from 1 to 20 and a letter from the alphabetF. 520 G. 260 H. 46 J. 4

9. The spinner at the right has an equal chance of landing on each number. Find P(6, then 6).

A. �419�

B. �211�

C. �110�

D. �27�

10. There are 5 peppermint, 4 licorice, 8 grape, 2 orange, and 9 cherry jelly beans in a bag. Paco picks a jelly bean. Without replacing the first one, he picks a second jelly bean. Find P(grape, then cherry).

F. �89� G. �2

21�

H. �11425�

J. �1125�

Use a tree diagram.

11. CLOTHING Janet has 4 blouses, 2 pairs of pants, and 3 pairs of socks that can be worn together. How many outfits can she make?A. 9 B. 18 C. 20 D. 24

12. TRAILS At Brand-X Ranch you can ride the Buckin’ Billy, Tennessee Lady, or Lag-Behind Nell. One trail goes through the woods, another goes up a mountain,and a third trail goes by a stream. How many different horse rides can you take?F. 3 G. 6 H. 9 J. 12

1

7

65

4

3

2

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 9 Test, Form 2AC

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.


Tell whether each problem represents a permutation (P) or a combination (C). Then solve the problem.

13. Twelve students remain in a game of tag. If 6 students go out in the next minute, how many different groups of six students can remain?A. C; 924 B. P; 1,140 C. C; 1,638 D. P; 665,280

14. Brandon has 8 different plates with which to set the table. How many different ways can he place the plates?F. C; 36 G. C; 336 H. P; 6,720 J. P; 40,320

15. In how many ways can Mia choose 10 mugs from a collection of 15?A. C; 360,360 B. C; 3,003 C. C; 150 D. P; 105

16. BAND How many ways can 7 clarinet players be seated in 7 chairs in the concert band?F. P; 56 G. C; 792 H. P; 5,040 J. C; 823,543

FOOTBALL Tori has four tickets to a football game. She can take three ofher friends with her, but five of her friends would like to go. They areTom, Jill, Joe, Marvin, and Ginger. To decide, Tori writes each of herfriends’ names on a separate piece of paper and selects one.

17. What is the probability that Tori picks a boy?

A. �15� B. �

25� C. �

35� D. �

23�

18. What is the probability that Tori picks someone whose name begins with theletter J?

F. �35� G. �

12� H. �

25� J. �

16�

19. If Tori draws a name 15 times and Tom’s name is picked five times, what is the experimental probability that Tom’s name is picked?

A. �55� B. �

56� C. �

13� D. �

15�

20. Choose the best comparison between the theoretical and experimental probability that Tom will go to the game. Use the experimental probability from Question 19.F. The theoretical probability is greater than the experimental probability.G. The theoretical probability is less than the experimental probability.H. The theoretical probability is equal to the experimental probability.J. The theoretical probability is not related to the experimental probability.

Bonus CLASSES Ishi can select 3 of her classes from the following options: French, Spanish, German, art, band,and consumer science. What is the probability that Ishi will select French, art, and band?

13.

14.

15.

16.

17.

18.

19.

20.

B:

NAME ________________________________________ DATE ______________ PERIOD _____


9 Chapter 9 Test, Form 2A (continued)C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.


1. How many different 5-letter passwords can be made using the letters A, E, I, O, and U if no letter is repeated?A. 4 B. 24 C. 25 D. 120


DOGS The boarders at a kennel are made up of the following dogs. If one dog is randomly selected for a 30-minute training session, find the probability of each event. The fractions are written in simplest form.

3. P(male)

A. �57� B. �

12� C. �1

52�

D. �254�

4. P(not retriever)

F. �58� G. �

13� H. �

14� J. �

18�

5. P(male or female)

A. 0 B. 1 C. �12� D. 24

For Questions 6–8, use the Fundamental Counting Principle to find the total number of outcomes in each situation.

6. tossing a dime, a quarter, a penny, and a nickel and rolling a number cubeF. 5 G. 14 H. 48 J. 96

7. choosing iced tea or lemonade, with lemon or lime twist, served in small,medium, or large size glassesA. 6 B. 7 C. 12 D. 24

8. picking a number from 1 to 30 and a letter from the alphabetF. 780 G. 390 H. 56 J. 4

9. The spinner at the right has an equal chance of landing on each number. Find P(an odd number, then an even number).

A. �77� B. �

1429�

C. �479�

D. �429�

10. There are 2 bunny counters, 16 mouse counters, 8 snake counters, and 7 monkey counters in the bag. Gina takes 2 counters without replacing the first counter. Find P(snake, then bunny).

F. �1616�

G. �116�

H. �313�

J. �616�

Use a tree diagram.

11. EQUIPMENT Raymond has 4 mouth guards, 5 pairs of shin guards, and 3 pairs of turf shoes. How many different combinations of sports equipment can he wear if he wears one of each type?A. 60 B. 50 C. 20 D. 15

1

7

65

4

3

2

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 9 Test, Form 2BC

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.


12. SPORTS If there are 8 footballs and 4 basketballs, how many different wayscould you choose 1 football and 1 basketball?F. 8 G. 12 H. 24 J. 32

Tell whether each problem represents a permutation (P) or a combination (C). Then solve the problem.13. Twenty students remain in a spelling bee. If 7 students misspell words in

the next round, how many different groups of 13 contestants can remain?A. C; 390,700,800 B. C; 77,520 C. P; 5,040 D. P; 1,820

14. How many different ways can Dana arrange 9 pairs of shoes in a row?F. C; 45 G. P; 3,039 H. C; 60,480 J. P; 362,880

15. In how many ways can Justin choose 11 cars from a collection of 20?A. P; 39,916,800 B. C; 167,960 C. C; 10,890 D. P; 110

16. How many different ways can Cora give 10 stuffed animals to the 10 guests at her birthday party?F. P; 3,628,800 G. P; 80,640 H. C; 65,978 J. C; 155

SOCCER Noriko has four tickets to a soccer game. She can take three of her friends with her, but seven would like to go. They are Isabel, Dan,Joni, Ike, Xavier, Patti, and Ian. To decide, Noriko writes each of her friends’ names on a separate piece of paper and selects one.17. What is the probability that Noriko picks a boy?

A. �23� B. �

47� C. �

37� D. �

17�

18. What is the probability that Noriko picks someone whose name begins with the letter I?

F. �27� G. �

37� H. �

47� J. �

57�

19. If Noriko draws a name 20 times and Patti’s name is picked six times, what is the experimental probability that Patti’s name is chosen?

A. �14� B. �1

30�

C. �270�

D. �67�

20. Choose the best comparison between the theoretical and experimental probability that Patti will go to the game. Use the experimental probability from Question 17.F. The theoretical probability is greater than the experimental probability.G. The theoretical probability is less than the experimental probability.H. The theoretical probability is equal to the experimental probability.J. The theoretical probability is not related to the experimental probability.

Bonus CLASSES Carol can select two classes from these options:French, Spanish, consumer science, industrial technology,art, and music. What is the probability that Carol will select industrial technology and music? B:

12.

13.

14.

15.

16.

17.

18.

19.

20.

NAME ________________________________________ DATE ______________ PERIOD _____


9 Chapter 9 Test, Form 2B (continued)C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

1. On another piece of paper, make a tree diagram to find how many different ways you can arrange the letters C, A, R, and S, if you use each letter once. How many ways are possible?

2. CRAFT Rodrigo is making round, square, and rectangular window ornaments. He cuts some from origami paper and others from old wallpaper. He then paints them either red or green. Make a tree diagram on another piece of paper to find how many different kinds of ornaments Rodrigo can make.What is the total number of ornaments?

Use the spinner to find each probability.Write as a fraction in simplest form.

3. P(even number)

4. P(2 or 3)

Use the Fundamental Counting Principle to find the total number of outcomes in each situation.

5. buying bedroom furniture if you can select one each from 7 dressers, 4 beds, 6 lamps, and 9 night tables

6. choosing one of each kind of pet from 8 hamsters, 3 guinea pigs, and 10 gerbils

7. the total number of sharks tagged in 6 days by 8 scientists if each scientist tags 3 new sharks every day

Tell whether each problem represents a permutation or a combination. Then solve the problem.

8. RACING In how many ways can 7 runners finish first,second, and third in a race?

9. How many different two-topping ice cream sundaes are available if there are 6 toppings to choose from?

10. In how many ways can you choose a committee of four people from the nine in the club?

11. How many different 3-digit codes can be created if no digit can be repeated?

8 1

5 4

27

36

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 9 Test, Form 2CC

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.

12. How many 6-digit numbers are there if no digit is repeated?

13. DESIGN In how many ways can you choose 2 colors for a design out of 14 colors?

CARPOOL Angie can fit 5 people in her van but 7 of her friends want to ride with her to the lacrosse game. Her friends are Sara, Penny, Geoff, Greg, Kimberly, Phil, and Lester. To decide, Angie writes each of her friends’ names on a separate piece of paper and selects one.

14. What is the probability that Angie picks a girl?

15. What is the probability that Angie picks someone whose name begins with the letter G or P?

16. If Angie picks a name 18 times and Sara’s name is picked 10 times, what is the experimental probability that Sara’s name is picked?

17. How does the theoretical probability that Sara will get a ride compare to the experimental probability in Question 16?


18. PENS Gwen has 4 blue pens, 8 black pens, 2 green pens, and 3 red pens in her desk drawer. She takes out two pens without replacing the first pen. Find P(green, then blue).

19. BEARS Giovanni has a bag of 17 wooden beads, 1 flowered bead, 4 tie-dyed beads, and 10 red beads. After replacing his first bead, he pulls out a second bead. Find P(tie-dyed,then flowered).

20. APPLES Melody’s dad brought home a crate of apples he picked from their orchards. The crate contained 10 Granny Smiths, 14 Red Delicious, 4 Golden Delicious, and 18 Braeburns.Without replacing the first apple, she took out a second apple. Find P(Golden Delicious, then Braeburn).

Bonus PASSWORDS Determine the number of passwords that can be made from 2 letters followed by 4 digits if no letter or digit can be used more than once.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

NAME ________________________________________ DATE ______________ PERIOD _____


9 Chapter 9 Test, Form 2C (continued)C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

1. On another piece of paper, make a tree diagram to find how many different ways you can arrange red, yellow, blue, and green colored pencils in a 4-pencil holder. How many arrangements are there?

2. LUNCH Barry sells hot dogs with or without mustard. Hiscustomers can also choose potato chips, corn chips, or pretzels.Make a tree diagram on another piece of paper to find out how many different orders Barry might receive if customers choose one type of hot dog and one type of chip or pretzel. How many different kinds of orders might Barry receive?


3. P(odd number)

4. P(4, or 5)


5. total number of trees planted in 5 days by 30 people, whoeach plant 3 trees per day

6. total number of disguises you can create with 2 different contact-lens colors, 3 different wigs, 2 different noses, and 1 mustache if one of each is chosen

7. choosing an outfit from 2 different hats, 3 pairs of pants,3 pairs of shoes, and a shirt if one of each is chosen


8. In how many ways can you select three classes from a total of 10 being offered?

9. How many ways can a president and vice-president bechosen from a committee of 8 members?

10. How many ways can 5 models line up to have their picture taken?

11. How many different 3-flavor shakes are available if there are 7 flavors of ice cream available?

8 1

5 4

27

36

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 9 Test, Form 2DC

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.


12. How many different 7-digit numbers are there if no digitsis repeated?

13. DESIGN In how many ways can you choose 3 colors for a design out of 11 colors?

CARPOOL Luis can fit 3 people in his car, including himself,but 5 of his friends want to ride with him to the track meet. His friends are Tim, Maria, Lilly, Katey, and Ruben.To decide, Luis writes each of his friends’ names on a separate piece of paper and selects one.

14. What is the probability that Luis picks a girl?

15. What is the probability that Luis picks someone whose name ends with the letter Y?

16. If Luis picks a name 12 times and Ruben’s name is picked 4 times, what is the experimental probability that Ruben’s name is picked?

17. How does the theoretical probability that Ruben will get a ride compare to the experimental probability in Question 16?


18. PETS Yvonne is playing with her gerbils. She has 4 white,3 brown, and 1 gray gerbil. Without replacing the first one,she takes a second gerbil out of the cage. Find P(white,then gray).

19. CLOTHES Andrew has 3 pairs of jeans shorts, 1 pair of camouflage shorts, and 2 pairs of black shorts in a drawer.He chooses one pair, puts them back and chooses another.Find P(jeans, then camouflage).

20. PUPPETS Shari has 4 lamb puppets, 5 horse puppets, and 2 dog puppets in a bag. Without replacing the first, she takes out a second puppet. Find P(horse, then lamb).

Bonus PASSWORDS Determine the number of passwords that can be made from 2 letters followed by 3 digits if no letter or digit can be used more than once.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

NAME ________________________________________ DATE ______________ PERIOD _____


9 Chapter 9 Test, Form 2D (continued)C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

1. On another piece of paper, make a tree diagram to find how many different ways you can arrange the numbers 1, 4, and 5 if no number can be used more than once. How many arrangements are there?

2. MUSIC Angela is deciding which song to play next. She can choose one that is fast or slow, current or old, and Country or Top 40. Make a tree diagram on another piece of paper to find how many types of songs she can choose from. How many types are there?


3. P(number less than 5)

4. P(even number or 7)


5. total number of toads found by 21 scientists in 3 days if each scientist finds 7 new toads each day

6. choosing one of each kind of ball from 4 glowballs,15 superballs, and 8 moonballs

7. choosing one of each color paint from 3 yellow paints,4 green paints, and 2 white paints


8. How many ways can 6 family photos be set in a line on a fireplace mantel?

9. How many different 4-topping salads are available if there are 8 toppings to choose from?

10. How many ways can you pick 3 kittens from a litter of 7 kittens?

11. How many different 3-letter security passwords can be created if no letter can be repeated?

8 1

5 4

27

36

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 9 Test, Form 3C

opyr

ight

©G

lenc

oe/M

cGra

w-H

ill,

a di

visi

on o

f The

McG

raw

-Hill

Com

pani

es,

Inc.


12. How many different passwords are there if the first two characters are two different letters and the last 4 characters are digits, where no digit is repeated?

13. FOOD In how many ways can you choose 3 side dishes from 12 choices?

CARPOOL Misu can fit 3 other people into his car but 5 of his friends want to get a ride to the baseball game. His friends are Brittany, Anne, Steve, Monique, and John. To decide,Misu writes each of his friends’ names on a separate piece of paper and selects one.

14. What is the probability that Misu picks a girl?

15. What is the probability that Misu picks someone whose name ends with the letter E?

16. If Misu chooses a name 16 times and Monique’s name is picked 6 times, what is the experimental probability that Monique’s name is picked?

17. How does the theoretical probability that Monique will get a ride compare to the experimental probability in Question 16?


18. BASKETBALL Rita has a record of making 2 out of every 5 free throws. What is the probability that she will make both of her next two free throws?

19. TESTS On a math test, 5 out of 20 students got an A. If three of the 20 students are chosen at random, what is the probability that all three got an A on the test?

20. Three cards are chosen at random from a standard deck of cards without replacement. What is the probability of getting 3 aces?

Bonus PASSWORDS Determine the number of passwords that can be made from 3 letters followed by 3 digits if no letter or digit can be used more than once and the digit 0 cannot be used.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

NAME ________________________________________ DATE ______________ PERIOD _____


9 Chapter 9 Test, Form 3 (continued)C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solutions in more than one wayor investigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.

1. Seven Oaks Middle School is having its Spring fair.

a. A game uses spinner A below. If a player spins a 1, he or she wins aprize. Explain how to find the theoretical probability of winning aprize.

Spinner A Spinner B

b. A second game uses spinner B. A player must spin a W to win.Explain how to find the experimental probability of spinning a W.

2. A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2)marbles.

a. Use a tree diagram to list all of the possible outcomes for tossing acoin and then drawing a marble from the bag.

b. Explain what is meant by independent events.

c. Find the probability of tossing a head and drawing a red marble.Explain you reasoning.

d. Find the probability of drawing two blue marbles if the first marble isnot replaced. Explain each step.

3. Rayna and her husband have 8 nieces, 9 nephews, 6 cousins, 3 aunts, and5 uncles.

a. Explain how you could use the Fundamental Counting Principle tofind how many ways Rayna could choose a team to play charades ifshe wants one of each type of relative on the team.

b. How many ways could just the nieces stand in line to limbo? Explainyour method.

c. If everyone except Rayna and her husband wants to play musicalchairs but there are only 10 chairs available, how many ways could 10of the relatives sit in the chairs when the music stops? Explain yourmethod.

W L

1 2

4 3

Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 9 Extended-Response Test

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1. Which equation could be used to find the width of a rectangle with a perimeter of 80 inches and a length of 25 inches? (Lesson 3-2)

A 80 � 25 � �w2� C 80 � 25 � w

B 80 � 50 � 2w D 80 � 50 � 2w

2. Solve w � 7.3 � 12.8. (Lesson 3-2)

F �20.1 G 5.5 H 14.6 J 20.1

3. Find the GCF of 30 and 42. (Lesson 4-2)

A 2 B 3 C 6 D 210

4. Write �290� as a percent. (Lesson 4-6)

F 0.45% G 4.5% H 45% J 450%

5. Find �196� � �

14

�. (Lesson 5-2)

A �14

� B �156� C �

12

� D �1136�

6. What is �38

� � �58

�? (Lesson 5-5)

F �1654� G �

35

� H �1156� J 1

7. Solve �12�k � �

27�. Check your solution. (Lesson 5-6)

A 7 B �74� C �

47� D �

17�

8. Write the ratio 2�23� yards to 4 feet as a fraction in simplest form.

(Lesson 6-1)

F �12� G �

23� H �

24.7� J �

21�

9. Solve the proportion: �83� � �

2w0�. (Lesson 6-5)

A �125�

B 1.2 C 7.5 D 53�13�

10. LAYAWAY Angie wants to put a winter coat on layaway at a store. To do so, she must pay the store 20% of the cost of the coat so they will hold it. If the coat costs $125, how much of a deposit does Angie need to pay the store? (Lesson 7-2)

F $250 G $25 H $12.50 J $2.50

11. Find the sales tax to the nearest cent on a $25 pair of shoes with 5.75% sales tax. (Lesson 7-7)

A $1.43 B $1.44 C $1.77 D $5.75

12. Find the simple interest to the nearest cent for a principal of $4,329, an interest rate of 9.25%, and a time period of 18 months. (Lesson 7-8)

F $7,207.79 G $4,929.94 H $4,356.25 J $600.65

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


9 Standardized Test Practice(Chapters 1–9)

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

13. SOFTWARE The data in the table shows the prices of the top-selling business software. Find the medianof the data. (Lesson 8-2)

A $53B $71.30C $183D $201

14. To determine the most popular kind of music in California,a survey of 100 randomly selected households in Sacramento is conducted. Of the households, 34 chose pop music. The researcher concluded that 34% of California households prefer pop music. Which of the following methods did the researcher use? (Lesson 8-8)

F simple random surveyG systematic random sampleH convenience sampleJ stratified random sample

15. GAMES Gene made up a game where each player tosses two coins and a number cube. Use a tree diagram to find how many outcomes are possible. (Lesson 9-2)

A 6 B 24 C 30 D 36

16. If there are 6 baseballs, 10 tennis balls, and 11 golf balls available, how many different combinations of balls could be made if one of each type is chosen? (Lesson 9-3)

F 660 G 66 H 60 J 27

17. SALAD BARS If Philip made three trips to a salad bar with 10 different items and chose only one different item each time, in how many ways could he have selected his food? (Lesson 9-5)

A 1,000 B 720 C 120 D 30

18. A water cooler holds 3 gallons of water.How many cups does the cooler hold? (Lesson 6-3)

F 12 G 24 H 48 J 60

19. How many different ways can 6 notebooks be arranged on a shelf? (Lesson 9-4)

A 4,320 B 720 C 216 D 36

13.

14.

15.

16.

17.

18.

19. A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

Standardized Test Practice (continued)

(Chapters 1–9)

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Software Prices ($)

218 .89 86 19

201 115 36 53

253 243

20. Find 3 � (�17). (Lesson 2-5)

21. Write 16% as a fraction in simplest form. (Lesson 4-6)

22. Find 2�34� � 2. Write in simplest form. (Lesson 5-7)

23. LANDFILLS The graph shows the content in U.S. landfills.How much more plastic isthere than food and yardwaste? (Lesson 8-4)

24. ASSIGNMENTS Linda must finish 7 projects from a list of 13for her industrial technology class. In how many ways canLinda do this if the order is not important? (Lesson 9-5)

25. PHOTOGRAPHY Paul is the photographer hired for a wedding.He is arranging 3 women, 3 men, and 2 children in a line for a picture. (Lesson 9-4)

a. How many ways can he arrange them if he wants them in the following order: child, woman, man, woman, man,woman, man, child? Explain.

b. How many ways can he arrange all of the people if the order of women, men, and children does not matter? Explain.

Other

Food

& Ya

rd W

aste

Rubb

er &

Leath

er

Metal

15

20

10

0

5

25

30

35

Perc

ent

Plasti

cPa

per

U.S. Landfill Content

8%

24%

6%

11%

30%

21%

Part 2: Short Response

Instructions: Write answers to short responses in the space provided.

20.

21.

22.

23.

24.

25a.

25b.

NAME ________________________________________ DATE ______________ PERIOD _____


9 Standardized Test Practice (continued)

(Chapters 1–9)

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

MILES PER HOUR For Questions 1–3, use the line plot that shows the speeds (in miles per hour) of 40 cars traveling on the freeway. (Lesson 2-3)

1. What is the range of the data?

2. What speed occurred most often?

3. Identify any clusters, gaps, or outliers.

4. RAINFALL The graph shows theaverage rainfall in Minneapolis,Minnesota, each month fromMarch to June. Predict theaverage rainfall for July.

5. Find the mean, median, and mode for the data.

$5, $9, $13, $7, $6, $5, $11

6. Make a stem-and-leaf plot for the data.

25, 35, 43, 50, 56,38, 45, 29, 40, 47

7. TESTS The data shows the quiz scores earned by students in a science class. What is the median?

8. TELEVISIONS The graph shows the countries withthe most televisions percapita. Why might thisgraph be consideredmisleading?

UKJapanCanadaUSA

700

900

800

600Tele

visi

ons

per 1

000

Peop

le

Australia

Countries with the MostTelevisions per Capita

Mar. Apr. May June

60

40

20

80

100

120

Aver

age

Rain

fall

(mm

)

Month

0

Rainfall in Minneapolis, MN

1.

2.

3.

4.

5.

6.

7.

8.

Ass

essm

ent


9NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Unit 4 Test(Chapters 8 and 9)

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

64 66 68 70 72 74 76 78 8062

�

��

��

��

��

��

��

��

��

��

��

Quiz Scores

18 17 20 10 1519 0 13 17 1417 20 11 10 9

9. A number cube is rolled two times. Find the probability of rolling an odd number then an even number.

10. A card is drawn from a standard deck of 52 cards.A second card is drawn without replacing the first card.Find P(black card, then red card).

For Questions 11–13, a set of 12 cards is numbered 1, 2, 3, ... , 12. Suppose you pick a card at random without looking. Find the probability of each event.Write as a fraction in simplest form.

11. P(5 or 7)

12. P(multiple of 3)

13. P(not an even number)

Use the spinner to find each probability. Write as a fractionin simplest form.

14. P(E)

15. P(not a vowel)

16. Make a tree diagram on another piece of paper to show the sample space for picking a number from 1 to 6 and choosing a color yellow, purple, or green. Then give the total number of outcomes.

17. Use the Fundamental Counting Principle to find the totalnumber of outcomes in the following situation. Find the totalnumber of cans of food donated to the Hunger Taskforce by40 people in 17 days if each person donates 2 cans every day.

For Questions 18 and 19, tell whether each problem represents a permutation or combination. Then solve the problem.

18. How many different ways can you choose 5 books from a total of 15 books?

19. How many different ways can 11 board games be stacked?

20. Tell whether the following event is independent or dependent.Then find the probability. Choose a particular male from 20 males and a particular female from 10 females.

A

E

F

C

B

D

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

NAME ________________________________________ DATE ______________ PERIOD _____


9 Unit 4 Test (continued)

(Chapters 8 and 9)

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

An

swer

s

pygp

Lesson 9–1

Cha

pter

99

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n a

t th

e to

p o

f p

age

460

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.W

hat

fra

ctio

n o

f th

e ta

ffy

is v

anil

la?

Wri

te i

n s

impl

est

form

.�1 8�

2.S

upp

ose

you

tak

e on

e pi

ece

of t

affy

fro

m t

he

box

wit

hou

t lo

okin

g.A

reyo

ur

chan

ces

of p

icki

ng

van

illa

th

e sa

me

as p

icki

ng

root

bee

r? E

xpla

in.

Sam

ple

an

swer

:Yes

;th

ere

is t

he

sam

e n

um

ber

of

van

illa

pie

ces

as r

oo

t b

eer

pie

ces.

Rea

d t

he

Less

on

Use

th

e in

form

atio

n f

rom

th

e in

trod

uct

ion

to

answ

er E

xerc

ises

3–5

.

3.H

ow d

o yo

u r

ead

P(c

her

ry)?

the

pro

bab

ility

of

pic

kin

g a

pie

ce o

fch

erry

taf

fy

4.P

(ch

erry

) �

� 46 8�;w

her

e do

es t

he

6 co

me

from

? W

her

e do

es t

he

48 c

ome

from

?6

�th

e n

um

ber

of

pie

ces

of

cher

ry t

affy

;48

�th

eto

tal n

um

ber

of

pie

ces

of

taff

y

5.P

roba

bili

ty c

an b

e w

ritt

en a

s a

frac

tion

,a d

ecim

al,o

r a

perc

ent.

Wri

teP

(ch

erry

) as

a d

ecim

al.

0.12

5

6.If

th

ere

is a

25%

ch

ance

th

at s

omet

hin

g w

ill

hap

pen

,wh

at i

s th

e ch

ance

that

it

wil

l n

oth

appe

n?

Wh

at a

re t

hes

e tw

o ev

ents

cal

led?

75%

;co

mp

lem

enta

ry e

ven

ts

Rem

emb

er W

hat

Yo

u L

earn

ed7.

Wri

te t

he

equ

atio

n P

(A)

�P

(not

A)

�1

in w

ords

.Wh

at d

oes

it m

ean

wit

hre

spec

t to

eve

nt

A?

Sam

ple

an

swer

:Th

e p

rob

abili

ty o

f A

eit

her

hap

pen

ing

or

no

t h

app

enin

g is

eq

ual

to

1;

it is

cer

tain

th

atev

ent

A w

ill e

ith

er h

app

en o

r n

ot

hap

pen

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

Sim

ple

Eve

nts

9-1

6SD

AP

3.3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Ant

icip

atio

n Gu

ide

Pro

bab

ility

Cha

pter

97

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Chapter Resources

pygp

9

Bef

ore

you

beg

in C

ha

pte

r 9

•R

ead

each

sta

tem

ent.

•D

ecid

e w

het

her

you

Agr

ee (

A)

or D

isag

ree

(D)

wit

h t

he

stat

emen

t.

•W

rite

A o

r D

in

th

e fi

rst

colu

mn

OR

if

you

are

not

su

re w

het

her

you

agr

ee o

r di

sagr

ee,w

rite

NS

(N

ot S

ure

).

Aft

er y

ou c

omp

lete

Ch

ap

ter

9

•R

erea

d ea

ch s

tate

men

t an

d co

mpl

ete

the

last

col

um

n b

y en

teri

ng

an A

or

a D

.

•D

id a

ny

of y

our

opin

ion

s ab

out

the

stat

emen

ts c

han

ge f

rom

th

e fi

rst

colu

mn

?

•F

or t

hos

e st

atem

ents

th

at y

ou m

ark

wit

h a

D,u

se a

pie

ce o

f pa

per

to w

rite

an

ex

ampl

e of

wh

y yo

u d

isag

ree.

Step

2

Step

1

ST

EP

1S

tate

men

tS

TE

P 2

A,D

,or

NS

A o

r D

1.T

he

prob

abil

ity

of a

n e

ven

t h

appe

nin

g is

a r

atio

th

at

com

pare

s th

e n

um

ber

of f

avor

able

ou

tcom

es t

o th

e n

um

ber

Dof

un

favo

rabl

e ou

tcom

es.

2.If

th

e pr

obab

ilit

y of

an

eve

nt

hap

pen

ing

is �3 5�

then

it

is m

ore

Ali

kely

for

th

e ev

ent

to h

appe

n t

han

to

not

hap

pen

.3.

In a

pro

babi

lity

exp

erim

ent,

a tr

ee d

iagr

am c

an b

e u

sed

to

Ash

ow a

ll t

he

poss

ible

ou

tcom

es.

4.T

he

Fu

nda

men

tal

Cou

nti

ng

Pri

nci

ple

stat

es t

hat

th

e n

um

ber

Dof

pos

sibl

e ou

tcom

es c

an a

lso

be f

oun

d by

div

isio

n.

5.T

o fi

nd

the

valu

e of

4!,

add

4�

3�

2�

1.D

6.In

a c

ombi

nat

ion

,ch

oosi

ng

even

t A

then

eve

nt

Bw

ould

be

Ath

e sa

me

as c

hoo

sin

g ev

ent

Bth

en e

ven

t A

.

7.T

he

expe

rim

enta

l pr

obab

ilit

y of

an

eve

nt

hap

pen

ing

wil

l al

way

s be

clo

se t

o th

e th

eore

tica

l pr

obab

ilit

y of

th

at e

ven

t D

hap

pen

ing.

8.T

he

act

it o

ut

stra

tegy

is

a go

od w

ay t

o so

lve

prob

lem

s be

cau

se t

he

resu

lts

wil

l be

th

e sa

me

ever

y ti

me

the

Dex

peri

men

t is

rep

eate

d.9.

A c

ompo

un

d ev

ent

con

sist

s of

tw

o or

mor

e si

mpl

e ev

ents

.A

10.

Th

e pr

obab

ilit

y of

tw

o in

depe

nde

nt

even

ts i

s fo

un

d th

e sa

me

Dw

ay a

s th

e pr

obab

ilit

y of

tw

o de

pen

den

t ev

ents

.

Answers (Anticipation Guide and Lesson 9-1)

Chapter 9 A1 Glencoe California Mathematics, Grade 6

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eS

imp

le E

ven

ts

Cha

pter

911

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–1

pygp

9-1

A s

et o

f 12

car

ds

is n

um

ber

ed 1

,2,3

,…12

.Su

pp

ose

you

pic

k a

car

d a

tra

nd

om w

ith

out

look

ing.

Fin

d t

he

pro

bab

ilit

y of

eac

h e

ven

t.W

rite

as

a fr

acti

on i

n s

imp

lest

for

m.

1.P

(5)

� 11 2�2.

P(6

or

8)�1 6�

3.P

(a m

ult

iple

of

3)�1 3�

4.P

(an

eve

n n

um

ber)

�1 2�

5.P

(a m

ult

iple

of

4)�1 4�

6.P

(les

s th

an o

r eq

ual

to

8)�2 3�

7.P

(a f

acto

r of

12)

�1 2�8.

P(n

ot a

mu

ltip

le o

f 4)

�3 4�

9.P

(1,3

,or

11)

�1 4�10

.P

(a m

ult

iple

of

5)�1 6�

Th

e st

ud

ents

at

Job

’s h

igh

sch

ool

wer

e su

rvey

ed t

o d

eter

min

e th

eir

favo

rite

foo

ds.

Th

e re

sult

s ar

esh

own

in

th

e ta

ble

at

the

righ

t.S

up

pos

e st

ud

ents

wer

e ra

nd

omly

sele

cted

an

d a

sked

wh

at t

hei

rfa

vori

te f

ood

is.

Fin

d t

he

pro

bab

ilit

yof

eac

h e

ven

t.W

rite

as

a fr

acti

on i

nsi

mp

lest

for

m.

11.

P(s

teak

)�1 5�

12.

P(s

pagh

etti

)� 43 0�

13.

P(c

erea

l or

sea

food

)�1 8�

14.

P(n

ot c

how

mei

n)

�7 8�

15.

P(p

izza

)�1 49 0�

16.

P(c

erea

l or

ste

ak)

� 49 0�

17.

P(n

ot s

teak

)�4 5�

18.

P(n

ot c

erea

l or

sea

food

)�7 8�

19.

P(c

hic

ken

)0

20.

P(c

how

mei

n o

r sp

agh

etti

)�1 5�

Fav

orit

e F

ood

Res

pon

ses

pizz

a19

stea

k8

chow

mei

n5

seaf

ood

4sp

agh

etti

3ce

real

16SDAP3.3

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Sim

ple

Eve

nts

Cha

pter

910

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

9-1

Wh

at i

s th

e p

rob

abil

ity

of r

olli

ng

a m

ult

iple

of

3 on

a n

um

ber

cu

be

mar

ked

wit

h 1

,2,3

,4,5

,an

d 6

on

its

fac

es.

P(m

ult

iple

of

3) �

��2 6�

Two

num

bers

are

mul

tiple

s of

3:3

and

6.

��1 3�

Sim

plify

.

Th

e pr

obab

ilit

y of

rol

lin

g a

mu

ltip

le o

f 3

is �1 3�

or a

bou

t 33

.3%

.

Wh

at i

s th

e p

rob

abil

ity

of n

otro

llin

g a

mu

ltip

le o

f 3

on a

nu

mb

ercu

be

mar

ked

wit

h 1

,2,3

,4,5

,an

d 6

on

its

fac

es?

P(A

) �

P(n

otA

) �

1

�1 3��

P(n

ot A

) �

1S

ubst

itute

�1 3�fo

r P

(A).

��1 3�

��1 3�

Sub

trac

t �1 3�

from

eac

h si

de�

��

��

��

�P

(not

A)

� �2 3�

Sim

plify

.

Th

e pr

obab

ilit

y of

not

roll

ing

a m

ult

iple

of

3 is

�2 3�or

abo

ut

66.7

%.

A s

et o

f 30

car

ds

is n

um

ber

ed 1

,2,3

,…,3

0.S

up

pos

e yo

u p

ick

a c

ard

at

ran

dom

wit

hou

t lo

okin

g.F

ind

th

e p

rob

abil

ity

of e

ach

eve

nt.

Wri

te a

sa

frac

tion

in

sim

ple

st f

orm

.

1.P

(12)

� 31 0�2.

P(2

or

3)� 11 5�

3.P

(odd

nu

mbe

r)�1 2�

4.P

(a m

ult

iple

of

5)�1 5�

5.P

(not

a m

ult

iple

of

5)�4 5�

6.P

(les

s th

an o

r eq

ual

to

10)

�1 3�

mu

ltip

les

of 3

pos

sibl

e�

��

tota

l n

um

bers

pos

sibl

e

The

pro

bab

ility

of a

sim

ple

even

t is

a r

atio

tha

t co

mpa

res

the

num

ber

of fa

vora

ble

outc

omes

to

the

num

ber

of p

ossi

ble

outc

omes

.Out

com

es o

ccur

at

ran

do

mif

each

out

com

e oc

curs

by

chan

ce.

Two

even

ts t

hat

are

the

only

one

s th

at c

an p

ossi

bly

happ

en a

re c

om

ple

men

tary

eve

nts

.The

sum

of

the

prob

abili

ties

of c

ompl

emen

tary

eve

nts

is 1

.

Exam

ple

1

Exam

ple

2

6SD

AP

3.3

Answers (Lesson 9-1)


An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Sim

ple

Eve

nts

Cha

pter

913

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–1

pygp

9-1

CO

INS

Su

san

op

ened

her

pig

gy b

ank

an

d c

oun

ted

the

nu

mb

er o

f ea

ch c

oin

.Th

e ta

ble

at

the

righ

tsh

ows

the

resu

lts.

For

Exe

rcis

es 1

–3,a

ssu

me

that

the

coin

s ar

e p

ut

in a

bag

an

d o

ne

is c

hos

en a

tra

nd

om.

1.W

hat

is

the

prob

abil

ity

that

a q

uar

ter

is c

hos

en?

�1 6�

2.W

hat

is

the

prob

abil

ity

that

a n

icke

l or

a di

me

is c

hos

en?

�4 93 0�

3.W

hat

is

the

prob

abil

ity

that

th

e ch

osen

coin

is

wor

th m

ore

than

5 c

ents

?

�2 5�

4.N

UM

BER

CU

BES

Juan

has

tw

o n

um

ber

cube

s,ea

ch w

ith

fac

es n

um

bere

d 1,

2,…

6.W

hat

is

the

prob

abil

ity

that

he

can

rol

l th

e cu

bes

so t

hat

th

e su

m o

fth

e fa

ces

show

ing

equ

als

11?

� 11 8�

5.SK

ATE

BO

AR

DS

Car

lott

a bo

ugh

t a

new

skat

eboa

rd f

or w

hic

h t

he

prob

abil

ity

ofh

avin

g a

defe

ctiv

e w

hee

l is

0.0

15.W

hat

is t

he

prob

abil

ity

of n

ot h

avin

g a

defe

ctiv

e w

hee

l?0.

985

6.C

ALC

ULA

TOR

SJa

ke’s

tea

cher

had

6ca

lcu

lato

rs f

or 2

8 st

ude

nts

to

use

.If

the

firs

t st

ude

nts

to

use

th

e ca

lcu

lato

rs a

rech

osen

at

ran

dom

,wh

at i

s th

epr

obab

ilit

y th

at J

ake

wil

l ge

t on

e?

� 13 4�

7.V

EHIC

LES

Th

e re

nta

l ca

r co

mpa

ny

had

14 s

edan

s an

d 8

min

ivan

s av

aila

ble

tore

nt.

If t

he

nex

t cu

stom

er p

icks

ave

hic

le a

t ra

ndo

m,w

hat

is

the

prob

abil

ity

that

a m

iniv

an i

s ch

osen

?

� 14 1�

8.M

USI

CT

ina

has

16

pop

CD

s,6

clas

sica

l,an

d 2

rock

.Tin

a ch

oose

s a

CD

at

ran

dom

.Wh

at i

s th

e pr

obab

ilit

ysh

e do

es n

ot c

hoo

se a

cla

ssic

al C

D?

�3 4�

Coi

nN

um

ber

quar

ters

15

dim

es21

nic

kels

22

pen

nie

s32

6SD

AP

3.3

A s

et o

f ca

rds

is n

um

ber

ed 1

,2,3

,… 2

4.S

up

pos

e yo

u p

ick

a c

ard

at

ran

dom

wit

hou

t lo

okin

g.F

ind

th

e p

rob

abil

ity

of e

ach

eve

nt.

Wri

te a

sa

frac

tion

in

sim

ple

st f

orm

.

1.P

(5)

2.P

(mu

ltip

le o

f 4)

3.P

(6 o

r 17

)

� 21 4��1 4�

� 11 2�

4.P

(not

equ

al t

o 15

)5.

P(n

ot a

fac

tor

of 6

)6.

P(o

dd n

um

ber)

�2 23 4��5 6�

�1 2�

CO

MM

UN

ITY

SER

VIC

ET

he

tab

le s

how

s th

e st

ud

ents

in

volv

ed i

nco

mm

un

ity

serv

ice.

Su

pp

ose

one

stu

den

t is

ran

dom

ly s

elec

ted

to

rep

rese

nt

the

sch

ool

at a

sta

te-w

ide

awar

ds

cere

mon

y.F

ind

th

ep

rob

abil

ity

of e

ach

eve

nt.

Wri

te a

s a

frac

tion

in

sim

ple

st f

orm

.

7.P

(boy

)�5 8�

8.P

(not

6th

gra

der)

�1 2�

9.P

(gir

l)

�3 8�10

.P

(8th

gra

der)

� 13 0�

11.

P(b

oy o

r gi

rl)

112

.P

(6th

or

7th

gra

der)

� 17 0�

13.

P(7

th g

rade

r)�1 5�

14.

P(n

ot a

9th

gra

der)

1

MEN

UA

del

icat

esse

n s

erve

s d

iffe

ren

t m

enu

ite

ms,

of w

hic

h 2

are

sou

ps,

6 ar

e sa

nd

wic

hes

,an

d 4

are

sal

ads.

How

lik

ely

is i

t fo

r ea

chev

ent

to h

app

en i

f yo

u c

hoo

se o

ne

item

at

ran

dom

fro

m t

he

men

u?

Exp

lain

you

r re

ason

ing.

15.

P(s

andw

ich

)�1 2�

16.

P(n

ot a

sou

p)�5 6�

17.

P(s

alad

)�1 3�

Th

ere

are

6 sa

nd

wic

h

Th

ere

are

2 so

up

T

her

e ar

e 4

sala

d

item

s o

f th

e 12

men

uit

ems.

So

th

ere

item

s o

f th

e 12

men

uit

ems.

are

10 n

on

-so

up

item

s.it

ems

of

the

12 m

enu

item

s.� 16 2�

��1 2�

�1 10 2��

�5 6�� 14 2�

��1 3�

18.

NU

MB

ER C

UB

EW

hat

is

the

prob

abil

ity

of r

olli

ng

an e

ven

nu

mbe

r or

a p

rim

e n

um

ber

on a

nu

mbe

r cu

be?

Wri

te a

s a

frac

tion

in

sim

ples

t fo

rm.

�5 6�

19.

CLO

SIN

G T

IME

At

a co

nve

nie

nce

sto

re t

her

e is

a 2

5% c

han

ce a

cu

stom

eren

ters

th

e st

ore

wit

hin

on

e m

inu

te o

f cl

osin

g ti

me.

Des

crib

e th

eco

mpl

emen

tary

eve

nt

and

fin

d it

s pr

obab

ilit

y.T

her

e is

a 7

5% c

han

cen

o c

ust

om

er w

ill e

nte

r w

ith

in o

ne

min

ute

of

clo

sin

g t

ime.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Sim

ple

Eve

nts

Cha

pter

912

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-1

Com

mu

nit

y S

ervi

cegi

rls

15bo

ys25

6th

gra

ders

207t

h g

rade

rs8

8th

gra

ders

12

6SD

AP

3.3



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

S

amp

le S

pac

es

Cha

pter

915

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–2

pygp

9-2

Get

Rea

dy

for

the

Less

on

Com

ple

te t

he

Min

i L

ab a

t th

e to

p o

f p

age

465

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.B

efor

e yo

u p

lay,

mak

e a

con

ject

ure

.Do

you

th

ink

that

eac

h p

laye

r h

as a

neq

ual

ch

ance

of

win

nin

g? E

xpla

in.

See

stu

den

ts’w

ork

.

2.N

ow,p

lay

the

gam

e.W

ho

won

? W

hat

was

th

e fi

nal

sco

re?

No

te:

Aft

er 2

0 to

sses

,th

e g

ames

may

be

tied

.Th

e n

um

ber

of

win

s fo

r ea

ch p

laye

r w

ill b

e ab

ou

t th

e sa

me.

Rea

d t

he

Less

on

3.H

ow d

oes

a tr

ee d

iagr

am r

esem

ble

a tr

ee?

Sam

ple

an

swer

:It

sta

rts

wit

h a

bas

e fo

r ea

ch e

ven

t (t

he

firs

t it

em o

n t

he

left

) an

d t

hen

bra

nch

es o

ut

to s

ho

w t

he

po

ssib

le o

utc

om

es f

or

the

even

t.4.

How

can

you

use

a t

able

to

fin

d th

e n

um

ber

of p

ossi

ble

outc

omes

of

anev

ent?

Sam

ple

an

swer

:C

ou

nt

the

nu

mb

er o

f en

trie

s lis

ted

inth

e tr

ee in

th

e sa

mp

le s

pac

e.5.

How

do

you

kn

ow t

he

gam

e pl

ayed

in

Exa

mpl

e 3

is f

air?

Sam

ple

answ

er:

Of

the

fou

r p

oss

ible

ou

tco

mes

,tw

o f

avo

r ea

ch p

laye

r.T

her

efo

re,t

he

pro

bab

ility

th

at e

ach

pla

yer

can

win

is 5

0%.

Rem

emb

er W

hat

Yo

u L

earn

ed6.

Dra

w a

tre

e di

agra

m t

hat

sh

ows

a fa

ir g

ame

that

is

diff

eren

t fr

om

the

exam

ples

in

you

r te

xtbo

ok.C

an y

ou t

hin

k of

a w

ay t

o dr

aw a

tr

ee d

iagr

am t

hat

sh

ows

a ga

me

that

is

not

fair

? M

ake

sure

you

in

clu

de a

des

crip

tion

if

the

gam

e is

not

cle

ar f

rom

you

r di

agra

m.

Sam

ple

an

swer

:Fa

ir g

ame:

Pla

yer

1 to

sses

a

coin

tw

ice.

Pla

yer

2 to

sses

a

coin

tw

ice.

Th

e p

laye

r th

at

get

s ta

ils t

he

mo

st w

ins.

Un

fair

gam

e:A

be,

Bet

ty,a

nd

C

arl e

ach

to

ss a

co

in.T

he

pla

yer

that

get

s ta

ils t

he

mo

st a

fter

3 t

oss

es w

ins.

Th

e p

laye

r w

ho

se n

ame

beg

ins

wit

h a

vo

wel

get

s o

nly

2 t

oss

es.

Toss

Third

Toss

Seco

ndTo

ssFi

rst

Spac

eSa

mpl

e

H TH

Abe

T

H H

H T

H T

T H

T T

H TH T

H T H T

H T

H T H T

H T

H

H H

TH

H H

H T

T

T H

HT

H T

T T

HT

T T

H TH T

H T H T

H T

H T H T

H H

HH

H T

H T

HH

T T

T H

HT

H T

T T

HT

T T

Betty

Carl

Unfa

ir Ga

me

6SD

AP

3.1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

914

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-1

Co

in-T

oss

ing

Exp

erim

ents

If a

coi

n i

s to

ssed

3 t

imes

,th

ere

are

8 po

ssib

le o

utc

omes

.Th

ey a

re l

iste

d in

th

eta

ble

belo

w.

On

ce a

ll t

he

outc

omes

are

kn

own

,th

e pr

obab

ilit

y of

an

y ev

ent

can

be

fou

nd.

For

exa

mpl

e,th

e pr

obab

ilit

y of

get

tin

g 2

hea

ds i

s �3 8�.

Not

ice

that

th

is i

s th

esa

me

as g

etti

ng

1 ta

il.

1.A

coi

n i

s to

ssed

4 t

imes

.Com

plet

e th

is c

har

t to

sh

ow t

he

poss

ible

outc

omes

.

2.W

hat

is

the

prob

abil

ity

of g

etti

ng

all

tail

s?� 11 6�

3.N

ow c

ompl

ete

this

tab

le.M

ake

char

ts l

ike

the

one

in E

xerc

ise

1 to

hel

pfi

nd

the

answ

ers.

Loo

k fo

r pa

tter

ns

in t

he

nu

mbe

rs.

4.W

hat

hap

pen

s to

th

e n

um

ber

of o

utc

omes

? th

e pr

obab

ilit

y of

all

tai

ls?

Sam

ple

an

swer

:It

is d

ou

blin

g;

it is

hal

vin

g.

Nu

mb

er o

f H

ead

s0

12

3

Ou

tcom

esT

TT

HT

TH

HT

HH

H

TH

TT

HH

TT

HH

TH

Nu

mb

er o

f H

ead

s0

12

3

Ou

tcom

esT

TT

TH

TT

TH

HT

TT

HH

H

TH

TT

HT

HT

HT

HH

TT

HT

TH

HT

HH

TH

HH

HH

4

TT

TH

TT

HH

HH

HT

TH

TH

HT

TH

Nu

mb

er o

f C

oin

Tos

ses

23

45

67

8

Tot

al O

utc

omes

48

1632

6412

825

6

Pro

bab

ilit

y of

Get

tin

g A

llT

ails

�1 4��1 8�

� 11 6�� 31 2�

� 61 4�� 11 28�

� 21 56�

6SD

AP

3.1

Answers (Lessons 9-1 and 9-2)


An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eS

amp

le S

pac

es

Cha

pter

917

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–2

pygp

9-2

Th

e sp

inn

er a

t th

e ri

ght

is s

pu

n t

wic

e.

1.D

raw

a t

ree

diag

ram

to

repr

esen

t th

e si

tuat

ion

.

2.W

hat

is

the

prob

abil

ity

of g

etti

ng

at

leas

t on

e A

?�5 9�

For

eac

h s

itu

atio

n,m

ake

a tr

ee d

iagr

am o

r ta

ble

to

show

th

esa

mp

le s

pac

e.T

hen

giv

e th

e to

tal

nu

mb

er o

f ou

tcom

es.

3.ch

oosi

ng

a h

ambu

rger

or

hot

dog

an

d po

tato

sal

ad o

r m

acar

oni

sala

d

Th

ere

are

4 p

oss

ible

ou

tco

mes

.

4.ch

oosi

ng

a vo

wel

fro

m t

he

wor

d C

OM

PU

TE

R

and

a co

nso

nan

t fr

om t

he

wor

d B

OO

K

Th

ere

are

6 p

oss

ible

o

utc

om

es.

5.ch

oosi

ng

betw

een

th

e n

um

bers

1,2

or

3,an

d th

e co

lors

blu

e,re

d,or

gre

en

Th

ere

are

9 p

oss

ible

o

utc

om

es.

blu

e

gre

en

red

1, g

reen

Num

ber

Sam

ple

Sp

ace

1, b

lue

1, r

ed

21 3

Co

lor

blu

e

gre

en

red

2, g

reen

2, b

lue

2, r

ed

blu

e

gre

en

red

3, g

reen

3, b

lue

3, r

ed

OB K

OK

OB

UB K

UK

UB

EB K

EK

EB

Vow

el f

rom

CO

MP

UT

ER

Co

nso

nan

tfr

om

BO

OK

Sam

ple

Sp

ace

ham

bur

ger

po

tato

mac

aro

niha

mb

urg

er, m

acar

oni

sal

ad

Ent

ree

Sal

adS

amp

le S

pac

e

ho

t d

og

po

tato

mac

aro

ni

hot

do

g, p

ota

to s

alad

ham

bur

ger

, po

tato

sal

ad

hot

do

g, m

acar

oni

sal

ad

A

A CB

A C

Sam

ple

Sp

ace

2nd

spin

1st

spin

A A

A B

B

A CB

B C

B A

B B

C

A CB

C C

C A

C B

B

CA

6SD

AP

3.1

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Sam

ple

Sp

aces

Cha

pter

916

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-2

WA

TCH

ESA

cer

tain

typ

e of

wat

ch c

omes

in

bro

wn

or

bla

ck a

nd

in

asm

all

or l

arge

siz

e.F

ind

th

e n

um

ber

of

colo

r-si

ze c

omb

inat

ion

s th

atar

e p

ossi

ble

.

Mak

e a

tabl

e to

sh

ow t

he

sam

ple

spac

e.T

hen

giv

e th

e to

tal

nu

mbe

r of

ou

tcom

es.

Th

ere

are

fou

r di

ffer

ent

colo

r an

d si

ze c

ombi

nat

ion

s.

CH

ILD

REN

Th

e ch

ance

of

hav

ing

eith

er a

boy

or

a gi

rl i

s 50

%.W

hat

is

the

pro

bab

ilit

y of

th

e S

mit

hs

hav

ing

two

girl

s?

Mak

e a

tree

dia

gram

to

show

th

e sa

mpl

e sp

ace.

Th

en f

ind

the

prob

abil

ity

of h

avin

g tw

o gi

rls.

Th

e sa

mpl

e sp

ace

con

tain

s 4

poss

ible

ou

tcom

es.O

nly

1 o

utc

ome

has

bot

h c

hil

dren

bei

ng

girl

s.S

o,th

e pr

obab

ilit

y of

hav

ing

two

girl

s is

�1 4�.

For

eac

h s

itu

atio

n,m

ake

a tr

ee d

iagr

am o

r ta

ble

to

show

th

e sa

mp

lesp

ace.

Th

en g

ive

the

tota

l n

um

ber

of

outc

omes

.

1.ch

oosi

ng

an o

utf

it f

rom

a g

reen

sh

irt,

blu

e sh

irt,

or a

red

sh

irt,

and

blac

kpa

nts

or

blu

e pa

nts

See

stu

den

ts’w

ork

.Th

ere

are

6 o

utc

om

es.

2.ch

oosi

ng

a vo

wel

fro

m t

he

wor

d C

OU

NT

ING

an

d a

con

son

ant

from

th

ew

ord

PR

IME

See

stu

den

ts’w

ork

.Th

ere

are

9 o

utc

om

es.

bo

yb

oy

gir

lb

oy,

gir

l

Ch

ild

1C

hil

d 2

Sam

ple

Sp

ace

gir

lb

oy

gir

l

gir

l, b

oy

bo

y, b

oy

gir

l, g

irl

A g

ame

in w

hich

pla

yers

of

equa

l ski

ll ha

ve a

n eq

ual c

hanc

e of

win

ning

is a

fai

r g

ame.

A t

ree

dia

gra

mor

tab

le is

use

d to

sho

w a

ll of

the

pos

sibl

e ou

tcom

es,

or s

amp

le s

pac

e, in

a p

roba

bilit

yex

perim

ent.

Col

orS

ize

Bro

wn

Sm

all

Bro

wn

Lar

ge

Bla

ckS

mal

l

Bla

ckL

arge

Exam

ple

1

Exam

ple

2

6SD

AP

3.1



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Sam

ple

Sp

aces

Cha

pter

919

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–2

pygp

9-2

1.G

ASO

LIN

EC

raig

sto

ps a

t a

gas

stat

ion

to f

ill

his

gas

tan

k.H

e m

ust

ch

oose

betw

een

fu

ll-s

ervi

ce o

r se

lf-s

ervi

ce a

nd

betw

een

reg

ula

r,m

idgr

ade,

and

prem

ium

gas

olin

e.D

raw

a t

ree

diag

ram

or

tabl

e sh

owin

g th

e po

ssib

leco

mbi

nat

ion

s of

ser

vice

an

d ga

soli

ne

type

.How

man

y po

ssib

le c

ombi

nat

ion

sar

e th

ere?

Th

ere

are

6 p

oss

ible

com

bin

atio

ns.

reg

ular

pre

miu

m

mid

gra

de

full,

pre

miu

m

Ser

vice

Sam

ple

Sp

ace

full,

reg

ular

full,

mid

gra

de

Sel

f

Ful

l

reg

ular

pre

miu

m

mid

gra

de

self,

pre

miu

m

self,

reg

ular

self,

mid

gra

de

Gas

olin

e

3.C

OIN

SIn

Exe

rcis

e 2,

wh

at i

s th

epr

obab

ilit

y of

get

tin

g 2

hea

ds,t

hen

2

tail

s?

� 11 6�

4.EQ

UIP

MEN

TT

he

com

pute

r ac

cess

ory

that

Joa

nn

e is

con

side

rin

g se

llin

g at

her

sto

re c

omes

in

wh

ite,

beig

e,gr

ay,

orbl

ack

and

as a

n o

ptic

al m

ouse

,m

ech

anic

al m

ouse

,or

trac

kbal

l.H

owm

any

com

bin

atio

ns

of c

olor

an

d m

odel

mu

st s

he

stoc

k in

ord

er t

o h

ave

at l

east

one

of e

very

pos

sibl

e co

mbi

nat

ion

?12

2.C

OIN

SJu

dy t

osse

s a

coin

4 t

imes

.Dra

wa

tree

dia

gram

or

tabl

e sh

owin

g th

epo

ssib

le o

utc

omes

.Wh

at i

s th

epr

obab

ilit

y of

get

tin

g at

lea

st 2

tai

ls? �1 11 6�

Four

thTo

ssT

hird

Toss

Sec

ond

Toss

Firs

tTo

ssS

pac

eS

amp

le

H TH T

H T H T

H T

H T H T

H H

T H

H H

H T

H H

H H

H H

T T

H T

H H

H T

H T

H T

T H

H T

T T

H TH T

H T H T

H T

H T H T

T H

H H

T H

H T

T H

T H

T H

T T

T T

H H

T T

H T

T T

T H

T T

T T

H T

6SD

AP

3.1

For

eac

h s

itu

atio

n,f

ind

th

e sa

mp

le s

pac

e u

sin

g a

tab

le o

r tr

eed

iagr

am.

1.ch

oosi

ng

blu

e,gr

een

,or

yell

ow w

all

pain

t w

ith

wh

ite,

beig

e,or

gra

ycu

rtai

ns

2.ch

oosi

ng

a lu

nch

con

sist

ing

of a

sou

p,sa

lad,

and

san

dwic

h f

rom

th

e m

enu

sh

own

in

th

e ta

ble.

3.G

AM

EK

imik

o an

d M

iko

are

play

ing

a ga

me

in w

hic

h e

ach

gir

l ro

lls

an

um

ber

cube

.If

the

sum

of

the

nu

mbe

rs i

s a

prim

e n

um

ber,

then

Mik

ow

ins.

Oth

erw

ise

Kim

iko

win

s.F

ind

the

sam

ple

spac

e.T

hen

det

erm

ine

wh

eth

er t

he

gam

e is

fai

r.

P(K

imik

o)�

�� 17 2�

;P

(Mik

o)

��

� 15 2�

Th

e g

ame

is n

ot

fair

sin

ce t

he

pro

bab

iliti

es a

re u

neq

ual

.

1 �

2 �

4 �

6 �

2�

��

363

�5

� 5

� 4

� 3

� 1

��

�36

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Sam

ple

Sp

aces

Cha

pter

918

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-2 S

oup

Sal

adS

and

wic

hT

orte

llin

iC

aesa

rR

oast

Bee

fL

enti

lM

acar

oni

Ham

Tu

rkey

Tort

ellin

iC

aesa

rR

oas

t B

eef

Tort

ellin

iC

aesa

rH

amTo

rtel

lini

Cae

sar

Turk

eyTo

rtel

lini

Mac

aro

ni

Ro

ast

Bee

fTo

rtel

lini

Mac

aro

ni

Ham

Tort

ellin

iM

acar

on

iTu

rkey

Len

til

Cae

sar

Ro

ast

Bee

fL

enti

lC

aesa

rH

amL

enti

lC

aesa

rTu

rkey

Len

til

Mac

aro

ni

Ro

ast

Bee

fL

enti

lM

acar

on

iH

amL

enti

lM

acar

on

iTu

rkey

sam

ple

an

swer

:

Sum

�2

Sum

�3

Sum

�4

Sum

�5

Sum

�6

Sum

�7

Sum

�8

Sum

�9

Sum

�10

Sum

�11

Sum

�12

1 �

1 =

22

�1

= 3

1 �

2 =

3

1 �

3 =

42

�2

= 4

3 �

1 =

4

1 �

4 =

52

�3

= 5

3 �

2 =

54

�1

= 5

1 �

5 =

62

�4

= 6

3 �

3 =

64

�2

= 6

5 �

1 =

6

1 �

6 =

72

�5

= 7

3 �

4 =

74

�3

= 7

5 �

2 =

76

�1

= 7

2 �

6 =

83

�5

= 8

4 �

4 =

85

�3

= 8

6 �

2 =

8

3 �

6 =

94

�5

= 9

5 �

4 =

96

�3

= 9

4�

6=

105

�5

=10

6+

4=

10

5�

6=

116

�5

=11

6�

6�

12

blu

e

blu

e p

aint

, whi

te c

urta

ins

blu

e p

aint

, bei

ge

curt

ains

blu

e p

aint

, gra

y cu

rtai

ns

whi

te

bei

ge

gra

y

gre

en p

aint

, whi

te c

urta

ins

gre

en p

aint

, bei

ge

curt

ains

gre

en p

aint

, gra

y cu

rtai

ns

whi

te

bei

ge

gra

y

yello

w p

aint

, whi

te c

urta

ins

yello

w p

aint

, bei

ge

curt

ains

yello

w p

aint

, gra

y cu

rtai

ns

whi

te

bei

ge

gra

y

gre

en

yello

w

Pai

ntS

amp

le S

pac

eC

urta

ins

6SD

AP

3.1



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

921

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–3

pygp

9-3

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n a

t th

e to

p o

f p

age

471

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.A

ccor

din

g to

th

e ta

ble,

how

man

y si

zes

of ju

nio

rs’ j

ean

s ar

e th

ere?

7

2.H

ow m

any

len

gth

s ar

e th

ere?

3

3.F

ind

the

prod

uct

of

the

two

nu

mbe

rs y

ou f

oun

d in

Exe

rcis

es 1

an

d 2.

21

4.D

raw

a t

ree

diag

ram

to

hel

p yo

u f

ind

the

nu

mbe

r of

dif

fere

nt

size

an

d le

ngt

h

com

bin

atio

ns.

How

doe

s th

e n

um

ber

of

outc

omes

com

pare

to

the

prod

uct

you

fo

un

d ab

ove?

Sam

ple

an

swer

:Th

ere

are

21 d

iffe

ren

t si

zes

and

len

gth

s o

f ju

nio

rs’j

ean

s.T

his

is t

he

sam

e as

th

e p

rod

uct

fo

un

d a

bov

e.

Rea

d t

he

Less

on

5.W

hat

ope

rati

on i

s u

sed

in t

he

Fu

nda

men

tal

Cou

nti

ng

Pri

nci

ple?

mu

ltip

licat

ion

6.H

ow i

s th

e in

form

atio

n i

n a

tre

e di

agra

m

or t

able

dif

fere

nt

from

th

e in

form

atio

n

prov

ided

by

cou

nti

ng?

Sam

ple

an

swer

:T

he

tree

dia

gra

m,i

n a

dd

itio

n t

oin

dic

atin

g t

he

tota

l nu

mb

er o

f p

oss

ible

o

utc

om

es,a

lso

list

s th

e o

utc

om

es

so t

hat

yo

u c

an s

ee t

he

con

ten

t o

f th

e o

utc

om

es a

s w

ell a

s th

eir

nu

mb

er.

Rem

emb

er W

hat

Yo

u L

earn

ed7.

Wri

te t

he

Fu

nda

men

tal

Cou

nti

ng

Pri

nci

ple

in y

our

own

wor

ds.

Sam

ple

an

swer

:If

eve

nt

Mca

n o

ccu

r in

mw

ays

and

isfo

llow

ed b

y ev

ent

Nth

at c

an o

ccu

r in

nw

ays,

then

th

e ev

ent

Mfo

llow

ed b

y N

can

occ

ur

in m

�n

way

s.

pet

ite

tall

reg

ular

3 ta

ll

Siz

esS

amp

le S

pac

e 3

pet

ite

3 re

gul

ar3

Leng

ths

pet

ite

tall

reg

ular

5 ta

ll

5 p

etite

5 re

gul

ar5

pet

ite

tall

reg

ular

7 ta

ll

7 p

etite

7 re

gul

ar7

pet

ite

tall

reg

ular

9 ta

ll

9 p

etite

9 re

gul

ar9

pet

ite

tall

reg

ular

11 t

all

11 p

etite

11 r

egul

ar11

pet

ite

tall

reg

ular

13 t

all

13 p

etite

13 r

egul

ar13

pet

ite

tall

reg

ular

15 t

all

15 p

etite

15 r

egul

ar15

6SD

AP

3.1

Less

on R

eadi

ng G

uide

Th

e F

un

dam

enta

l Co

un

tin

g P

rin

cip

le

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

920

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-2

Pro

bab

iliti

es a

nd

Reg

ion

sT

he

spin

ner

at

the

righ

t ca

n b

e u

sed

to i

ndi

cate

th

at t

he

prob

abil

ity

of

lan

din

g in

eit

her

of

two

regi

ons

is �1 2�.

P(A

) �

�1 2�P

(B)

� �1 2�

Rea

d t

he

des

crip

tion

of

each

sp

inn

er.U

sin

g a

pro

trac

tor

and

ru

ler,

div

ide

each

sp

inn

er i

nto

reg

ion

s th

at s

how

th

e in

dic

ated

pro

bab

ilit

y.

1.T

wo

regi

ons

A a

nd

B:t

he

prob

abil

ity

of l

andi

ng

in r

egio

n A

is

�3 4�.

Wh

at i

s th

e pr

obab

ilit

y of

lan

din

g in

reg

ion

B?

P(B

) �

�1 4�

2.T

hre

e re

gion

s A

,B,a

nd

C:t

he

prob

abil

ity

of l

andi

ng

in r

egio

n A

is �1 2�

and

the

prob

abil

ity

of l

andi

ng

in r

egio

n B

is

�1 4�.W

hat

is

the

prob

abil

ity

of l

andi

ng

in r

egio

n C

?

P(C

) �

�1 4�

3.T

hre

e re

gion

s A

,B,a

nd

C:t

he

prob

abil

ity

of l

andi

ng

in r

egio

n A

is �3 8�

and

the

prob

abil

ity

of l

andi

ng

in r

egio

n B

is

�1 8�.W

hat

is

the

prob

abil

ity

of l

andi

ng

in r

egio

n C

?

P(C

) �

�1 2�

4.F

our

regi

ons

A,B

,C,a

nd

D:t

he

prob

abil

ity

of l

andi

ng

in r

egio

n A

is � 11 6�

,th

e pr

obab

ilit

y of

lan

din

g in

reg

ion

B i

s �1 8�,

and

the

prob

abil

ity

of l

andi

ng

in r

egio

n C

is

�1 4�.W

hat

is

the

prob

abil

ity

of l

andi

ng

in

regi

on D

?

P(D

) �

� 19 6�

5.T

he

spin

ner

at

the

righ

t is

an

equ

ilat

eral

tri

angl

e,di

vide

d in

to

regi

ons

by l

ine

segm

ents

th

at d

ivid

e th

e si

des

in h

alf.

Is t

he

spin

ner

div

ided

in

to r

egio

ns

of e

qual

pro

babi

lity

?ye

s

BCD

A

BC

A

C

A

BB

A

A

B

6SDAP3.1



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

923

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–3

pygp

9-3

Use

th

e F

un

dam

enta

l C

oun

tin

g P

rin

cip

le t

o fi

nd

th

e to

tal

nu

mb

er o

fou

tcom

es i

n e

ach

sit

uat

ion

.

1.ro

llin

g tw

o n

um

ber

cube

s an

d to

ssin

g on

e co

in72

2.ch

oosi

ng

rye

or B

erm

uda

gra

ss a

nd

3 di

ffer

ent

mix

ture

s of

fer

tili

zer

6

3.m

akin

g a

san

dwic

h w

ith

ham

,tu

rkey

,or

roas

t be

ef;S

wis

s or

pro

volo

ne

chee

se;a

nd

mu

star

d or

may

onai

se12

4.to

ssin

g 4

coin

s16

5.ch

oosi

ng

from

3 s

izes

of

dist

ille

d,fi

lter

ed,o

r sp

rin

g w

ater

9

6.ch

oosi

ng

from

3 f

lavo

rs o

f ju

ice

and

3 si

zes

9

7.ch

oosi

ng

from

35

flav

ors

of i

ce c

ream

;on

e,tw

o,or

th

ree

scoo

ps;a

nd

suga

ror

waf

fle

con

e21

0

8.pi

ckin

g a

day

of t

he

wee

k an

d a

date

in

th

e m

onth

of A

pril

210

9.ro

llin

g 3

nu

mbe

r cu

bes

and

toss

ing

2 co

ins

864

10.

choo

sin

g a

4-le

tter

pas

swor

d u

sin

g on

ly v

owel

s62

5

11.

choo

sin

g a

bicy

cle

wit

h o

r w

ith

out

shoc

k ab

sorb

ers;

wit

h o

r w

ith

out

ligh

ts;a

nd

5 co

lor

choi

ces

20

12.

a li

cen

se p

late

th

at h

as 3

nu

mbe

rs f

rom

0 t

o 9

and

2 le

tter

s67

6,00

06SD

AP

3.1

Skill

s Pr

actic

e T

he

Fu

nd

amen

tal C

ou

nti

ng

Pri

nci

ple

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

922

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-3

CLO

THIN

GA

nd

y h

as 5

sh

irts

,3 p

airs

of

pan

ts,a

nd

6 p

airs

of

sock

s.H

ow m

any

dif

fere

nt

outf

its

can

An

dy

choo

se w

ith

a s

hir

t,p

air

ofp

ants

,an

d p

air

of s

ock

s?

An

dy c

an c

hoo

se 9

0 di

ffer

ent

outf

its.

Use

th

e F

un

dam

enta

l C

oun

tin

g P

rin

cip

le t

o fi

nd

th

e to

tal

nu

mb

er o

fou

tcom

es i

n e

ach

sit

uat

ion

.

1.ro

llin

g tw

o n

um

ber

cube

s36

2.to

ssin

g 3

coin

s8

3.pi

ckin

g on

e co

nso

nan

t an

d on

e vo

wel

105

4.ch

oosi

ng

one

of 3

pro

cess

or s

peed

s,2

size

s of

mem

ory,

and

4 si

zes

of

har

d dr

ive

24

5.ch

oosi

ng

a 4-

,6-,

or 8

-cyl

inde

r en

gin

e an

d 2-

or

4-w

hee

l dr

ive

6

6.ro

llin

g 2

nu

mbe

r cu

bes

and

toss

ing

2 co

ins

144

7.ch

oosi

ng

a co

lor

from

4 c

olor

s an

d a

nu

mbe

r fr

om 4

to

1028

If ev

ent

Mca

n oc

cur

in m

way

s an

d is

follo

wed

by

even

t N

that

can

occ

ur in

nw

ays,

the

n th

e ev

ent

Mfo

llow

ed b

y N

can

occu

r in

m�

nw

ays.

Thi

s is

cal

led

the

Fu

nd

amen

tal C

ou

nti

ng

Pri

nci

ple

.

num

ber

of s

hirt

snu

mbe

r of

pan

tsnu

mbe

r of

soc

ksto

tal n

umbe

r of

out

fits

�

�

�

�

5�

3�

6�

90

Exam

ple

1

6SD

AP

3.1

Stud

y Gu

ide

and

Inte

rven

tion

Th

e F

un

dam

enta

l Co

un

tin

g P

rin

cip

le



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

925

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–3

pygp

9-3

1.SU

RFB

OA

RD

Jay

own

s 3

surf

boar

ds a

nd

2 w

etsu

its.

If h

e ta

kes

one

surf

boar

dan

d on

e w

etsu

it t

o th

e be

ach

,how

man

y di

ffer

ent

com

bin

atio

ns

can

he

choo

se?

6

2.SH

OPP

ING

Joh

n i

s tr

yin

g to

dec

ide

wh

ich

bag

of

dog

food

to

buy.

Th

e br

and

he

wan

ts c

omes

in

4 f

lavo

rs a

nd

3 si

zes.

How

man

y ch

oice

s ar

e th

ere?

12

3.LO

TTER

YT

o pu

rch

ase

a lo

tter

y ti

cket

,yo

u m

ust

sel

ect

4 n

um

bers

fro

m 0

to

9.H

ow m

any

poss

ible

lot

tery

tic

kets

can

be c

hos

en?

10,0

00

4.R

ESTA

UR

AN

TSM

iria

m’s

fav

orit

ere

stau

ran

t h

as 3

spe

cial

s ev

ery

day.

Eac

h s

peci

al h

as 2

ch

oice

s of

veg

etab

lean

d 3

choi

ces

of d

esse

rt.H

ow m

any

diff

eren

t m

eals

cou

ld M

iria

m h

ave?

18

5.R

OU

TES

Wh

en S

un

il g

oes

to t

he

buil

din

g w

her

e h

e w

orks

,he

can

go

thro

ugh

4 d

iffe

ren

t do

ors

into

th

e lo

bby.

Th

en h

e ca

n g

o to

th

e se

ven

th f

loor

by

taki

ng

2 di

ffer

ent

elev

ator

s or

2di

ffer

ent

stai

rway

s.H

ow m

any

diff

eren

t w

ays

can

Su

nil

get

fro

mou

tsid

e th

e bu

ildi

ng

to t

he

seve

nth

floo

r?16

6.ST

EREO

SJa

ilin

wen

t to

her

loc

al s

tere

ost

ore.

Giv

en h

er b

udg

et a

nd

the

avai

labl

e se

lect

ion

,sh

e ca

n c

hoo

sebe

twee

n 2

CD

pla

yers

,5 a

mpl

ifie

rs,

and

3 pa

irs

of s

peak

ers.

How

man

ydi

ffer

ent

ster

eos

can

Jai

lin

pu

rch

ase?

30

7.D

ESSE

RT

For

des

sert

you

can

ch

oose

appl

e,ch

erry

,blu

eber

ry,o

r pe

ach

pie

to

eat,

and

mil

k or

juic

e to

dri

nk.

How

man

y di

ffer

ent

com

bin

atio

ns

can

you

choo

se f

rom

?8

8.TE

STS

Joh

n i

s ta

kin

g a

tru

e or

fal

sequ

iz.T

her

e ar

e si

x qu

esti

ons

on t

he

quiz

.How

man

y w

ays

can

th

e qu

iz b

ean

swer

ed?

64

6SD

AP

3.1

Wor

d Pr

oble

m P

ract

ice

Th

e F

un

dam

enta

l Co

un

tin

g P

rin

cip

leU

se t

he

Fu

nd

amen

tal

Cou

nti

ng

Pri

nci

ple

to

fin

d t

he

tota

l n

um

ber

of

outc

omes

in

eac

h s

itu

atio

n.

1.ch

oosi

ng

from

8 c

ar m

odel

s,5

exte

rior

pai

nt

colo

rs,a

nd

2 in

teri

or c

olor

s80

2.se

lect

ing

a ye

ar i

n t

he

last

dec

ade

and

a m

onth

of

the

year

1

20

3.pi

ckin

g fr

om 3

th

eme

park

s an

d 1-

day,

2-da

y,3-

day,

and

5-da

y pa

sses

1

2

4.ch

oosi

ng

a m

eat

and

chee

se s

andw

ich

fr

om t

he

list

sh

own

in

th

e ta

ble

16

5.to

ssin

g a

coin

an

d ro

llin

g 2

nu

mbe

r cu

bes

72

6.se

lect

ing

coff

ee i

n r

egu

lar

or d

ecaf

,wit

h o

r w

ith

out

crea

m,a

nd

wit

h o

rw

ith

out

swee

ten

ers

8

7C

OIN

SF

ind

the

nu

mbe

r of

pos

sibl

e ou

tcom

es i

f 2

quar

ters

,4 d

imes

,an

d 1

nic

kel

are

toss

ed.

27�

128

8.SO

CIA

L SE

CU

RIT

YF

ind

the

nu

mbe

r of

pos

sibl

e 9-

digi

t so

cial

sec

uri

tyn

um

bers

if

the

digi

ts m

ay b

e re

peat

ed.

109

or

1,00

0,00

0,00

0

9.A

IRPO

RTS

Jolo

n w

ill

be s

tayi

ng

wit

h h

is g

ran

dpar

ents

for

a w

eek.

Th

ere

are

fou

r fl

igh

ts t

hat

lea

ve t

he

airp

ort

nea

r Jo

lon

's h

ome

that

con

nec

t to

an a

irpo

rt t

hat

has

tw

o di

ffer

ent

flig

hts

to

his

gra

ndp

aren

ts’ h

omet

own

.F

ind

the

nu

mbe

r of

pos

sibl

e fl

igh

ts.T

hen

fin

d th

e pr

obab

ilit

y of

tak

ing

the

earl

iest

fli

ght

from

eac

h a

irpo

rt i

f th

e fl

igh

t is

sel

ecte

d at

ran

dom

.

8;�1 8�

10.

AN

ALY

ZE T

AB

LES

Th

e ta

ble

show

s th

e ki

nds

of

hom

es o

ffer

ed b

y a

resi

den

tial

bu

ilde

r.If

th

e bu

ilde

r of

fers

a d

isco

un

t on

on

e h

ome

at r

ando

m,f

ind

the

prob

abil

ity

it w

ill

be a

4-b

edro

om

hom

e w

ith

an

ope

n p

orch

.Exp

lain

yo

ur

reas

onin

g.

Sam

ple

an

swer

:Th

e bu

ilder

off

ers

3�

4 �

2 �

24 k

ind

s o

fh

om

es.T

he

dis

cou

nte

d h

om

e h

as 1

ch

oic

e fo

r th

e n

um

ber

o

f b

edro

om

s,4

cho

ices

fo

r th

e st

yle

of

kitc

hen

,an

d 1

ch

oic

efo

r th

e ty

pe

of

po

rch

.Sin

ce 1

�4

�1

�4,

the

pro

bab

ility

is � 24 4�

��1 6� .

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

924

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-3

Nu

mb

er o

f S

tyle

of

Typ

e of

Bed

room

sK

itch

enP

orch

5-be

droo

mM

edit

erra

nea

nO

pen

4-be

droo

mC

onte

mpo

rary

Scr

een

3-be

droo

mS

outh

wes

tern

Col

onia

l

Ch

eese

Mea

tP

rovo

lon

eS

alam

iS

wis

sT

urk

eyA

mer

ican

Tu

na

Ch

edda

rH

am

6SD

AP

3.1

Prac

tice

Th

e F

un

dam

enta

l Co

un

tin

g P

rin

cip

le



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

Per

mu

tati

on

s

Cha

pter

927

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–4

pygp

9-4

Get

Rea

dy

for

the

Less

on

Com

ple

te t

he

Min

i L

ab a

t th

e to

p o

f p

age

475

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.W

hen

you

fir

st s

tart

ed t

o m

ake

you

r li

st,h

ow m

any

choi

ces

did

you

hav

efo

r yo

ur

firs

t cl

ass?

3

2.O

nce

you

r fi

rst

clas

s w

as s

elec

ted,

how

man

y ch

oice

s di

d yo

u h

ave

for

the

seco

nd

clas

s? T

hen

,th

e th

ird

clas

s?2;

1

Rea

d t

he

Less

on

3.E

xpla

in w

hy

the

arra

nge

men

t S

cien

ce,M

ath

,Lan

guag

e A

rts

is a

perm

uta

tion

of

Mat

h,S

cien

ce,L

angu

age

Art

s.T

he

ord

er o

f th

ecl

asse

s is

dif

fere

nt.

4.In

Exa

mpl

e 1

on p

age

475,

wh

y is

th

ere

only

1 c

hoi

ce f

or t

he

thir

d cl

ass?

Sam

ple

an

swer

:S

ince

th

ere

are

on

ly t

hre

e cl

asse

s,o

nly

1ch

oic

e re

mai

ns

for

the

thir

d c

lass

.

5.In

Exa

mpl

e 2

on p

age

476,

wh

y ar

e th

ere

only

7 c

hoi

ces

for

seco

nd

plac

e?S

amp

le a

nsw

er:T

her

e ar

e o

nly

8 s

wim

mer

s,an

d o

ne

of

them

com

es in

fir

st p

lace

.Th

at p

erso

n c

ann

ot

com

e in

sec

on

dp

lace

as

wel

l.S

o,t

her

e ar

e o

nly

7 s

wim

mer

s le

ft

that

co

uld

co

me

in s

eco

nd

pla

ce.

Rem

emb

er W

hat

Yo

u L

earn

ed6.

Loo

k u

p th

e w

ord

perm

ute

in a

dic

tion

ary.

How

doe

s th

e m

ean

ing

of t

his

wor

d re

late

to

the

con

cept

s in

th

is l

esso

n,e

spec

iall

y th

e co

nce

pt o

fpe

rmu

tati

ons?

Sam

ple

an

swer

:Th

e w

ord

per

mu

te m

ean

s to

arra

ng

e in

all

po

ssib

le w

ays.

A p

erm

uta

tio

n is

th

e lis

tin

g o

fal

l of

thes

e ar

ran

gem

ents

.

6SDAP3.1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

926

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-3

Cu

rio

us

Cu

bes

If a

six

-fac

ed c

ube

is

roll

ed a

ny

nu

mbe

r of

tim

es,t

he

theo

reti

cal

prob

abil

ity

ofth

e cu

be l

andi

ng

on a

ny

give

n f

ace

is �1 6�.

Eac

h c

ub

e b

elow

has

six

fac

es a

nd

has

bee

n r

olle

d 1

00 t

imes

.Th

eou

tcom

es h

ave

bee

n t

alli

ed a

nd

rec

ord

ed i

n a

fre

qu

ency

tab

le.B

ased

on t

he

dat

a in

eac

h f

req

uen

cy t

able

,wh

at c

an y

ou s

ay a

re p

rob

ably

on t

he

un

seen

fac

es o

f ea

ch c

ub

e?

1.

Th

e fa

ces

are

nu

mb

ered

2,

3,an

d 6

.

2.T

her

e ar

e tw

o y

ello

wfa

ces

and

on

e re

d f

ace.

3.

Th

e fa

ces

are

bla

nk.

4.

Th

e fa

ces

are

nu

mb

ered

1,

4,an

d 5

.

5.

On

e fa

ce is

nu

mb

ered

2

and

tw

o f

aces

are

b

lan

k.1

4

5

14

5

Blue

Red

Red

Yello

wBlue

Red

14

5O

utc

ome

Tal

ly1

152

143

184

165

196

18

Ou

tcom

eT

ally

blu

e17

red

30

yell

ow53

Ou

tcom

eT

ally

red

30

blu

e16

blan

k54

Ou

tcom

eT

ally

134

432

534

Ou

tcom

eT

ally

114

513

418

216

blan

k39

6SD

AP

3.1



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eP

erm

uta

tio

ns

Cha

pter

929

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–4

pygp

9-4

Fin

d t

he

valu

e of

eac

h e

xpre

ssio

n.

1.2

· 12

2.4

· 3 ·

2 · 1

24

3.3

· 2 ·

1 · 5

· 4

· 3 ·

2 · 1

720

4.9

· 8 ·

7 · 6

· 5

· 4 ·

3 · 2

· 1

362,

880

5.2

· 1 ·

8 · 7

· 6

· 5 ·

4 · 3

· 2

· 180

,640

6.3

· 2 ·

1 · 2

· 1

12

7.11

· 10

· 9

990

8.10

· 9

· 8 ·

7 · 6

· 5

· 4 ·

3 · 2

· 1

3,62

8,80

0

9.5

· 4 ·

3 · 2

· 1

· 2 ·

124

010

.5

· 4 ·

3 · 2

120

11.

8 · 7

· 6

· 5 ·

4 · 3

· 2

· 140

,320

12.

6 · 5

· 4

· 3 ·

2 · 1

720

13.

How

man

y w

ays

can

you

arr

ange

th

e le

tter

s in

th

e w

ord

PR

IME

?12

0

14.

How

man

y w

ays

can

you

arr

ange

8 d

iffe

ren

t cr

ates

on

a s

hel

f if

th

ey a

repl

aced

fro

m l

eft

to r

igh

t?40

,320

6SDAP3.1

Exer

cise

s

Exam

ple

2

Exam

ple

3

Exam

ple

1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Per

mu

tati

on

s

Cha

pter

928

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-4

Fin

d t

he

valu

e of

5 �

4 �

3 �

2 �

1.

5�

4�

3�

2�

1�

120

Sim

plify

.

Fin

d t

he

valu

e of

4 �

3�

2 �

1 �

2 �

1.

4�

3�

2�

1�

2�

1�

48S

impl

ify.

BO

OK

SH

ow m

any

way

s ca

n 4

dif

fere

nt

boo

ks

be

arra

nge

d o

n a

boo

ksh

elf?

Th

is i

s a

perm

uta

tion

.Su

ppos

e th

e bo

oks

are

plac

ed o

n t

he

shel

f fr

om l

eft

to r

igh

t.T

here

are

4ch

oice

s fo

r th

e fir

st b

ook.

The

re a

re 3

choi

ces

that

rem

ain

for

the

seco

nd b

ook.

The

re a

re 2

choi

ces

that

rem

ain

for

the

third

boo

k.T

here

is 1

choi

ce t

hat

rem

ains

for

the

four

th b

ook.

4�

3�

2�

1�

24

Sim

plify

.

So,

ther

e ar

e 24

way

s to

arr

ange

4 d

iffe

ren

t bo

oks

on a

boo

ksh

elf.

Fin

d t

he

valu

e of

eac

h e

xpre

ssio

n.

1.3

· 2 ·

16

2.7

· 6 ·

5 · 4

· 3

· 2 ·

15,

040

3.6

· 5 ·

4 · 3

· 2

· 1 ·

3 · 2

· 1

4,32

04.

9 · 8

· 7

504

5.H

ow m

any

way

s ca

n y

ou a

rran

ge t

he

lett

ers

in t

he

wor

d G

RO

UP

?12

0

6.H

ow m

any

diff

eren

t 4-

digi

t n

um

bers

can

be

crea

ted

if n

o di

git

can

be

repe

ated

? R

emem

ber,

a n

um

ber

can

not

beg

in w

ith

0.

4,53

6

A p

erm

uta

tio

nis

an

arra

ngem

ent,

or li

stin

g, o

f ob

ject

s in

whi

ch o

rder

is im

port

ant.

You

can

use

the

Fun

dam

enta

l Cou

ntin

g P

rinci

ple

to f

ind

the

num

ber

of p

ossi

ble

arra

ngem

ents

.

6SDAP3.1



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Per

mu

tati

on

s

Cha

pter

931

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–4

pygp

9-4

1.A

REA

CO

DES

How

man

y di

ffer

ent

3-di

git

area

cod

es c

an b

e cr

eate

d if

no

digi

t ca

n b

e re

peat

ed?

720

2.C

AR

DS

Jaso

n i

s de

alt

five

pla

yin

gca

rds.

In h

ow m

any

diff

eren

t or

ders

cou

ld J

ason

hav

e be

en d

ealt

th

e sa

me

han

d?12

0

3.PA

SSW

OR

DS

How

man

y di

ffer

ent

3-le

tter

pas

swor

ds a

re p

ossi

ble

if n

ole

tter

may

be

repe

ated

?15

,600

4.R

AC

ING

All

22

stu

den

ts i

n A

my’

s cl

ass

are

goin

g to

ru

n t

he

100-

met

er d

ash

.In

how

man

y w

ays

can

th

e st

ude

nts

fin

ish

in f

irst

,sec

ond,

and

thir

d pl

ace?

9,24

0

5.LE

TTER

SH

ow m

any

way

s ca

n y

ouar

ran

ge t

he

lett

ers

in t

he

wor

dH

IST

OR

Y?

5,04

0

6.PA

RK

ING

Th

e pa

rkin

g lo

t fo

r a

com

pan

yh

as t

hre

e pa

rkin

g sp

aces

for

com

pact

cars

.Th

e co

mpa

ny

has

8 e

mpl

oyee

sw

ith

com

pact

car

s.H

ow m

any

way

s ca

nth

e co

mpa

ct p

arki

ng

spac

es b

e fi

lled

?33

6

7.SE

RIA

L N

UM

BER

SH

ow m

any

diff

eren

t 6-

digi

t se

rial

nu

mbe

rs a

re a

vail

able

if

no

digi

t ca

n b

e re

peat

ed?

151,

200

8.W

INN

ERS

Th

ere

are

156

way

s fo

r 2

cars

to w

in f

irst

an

d se

con

d pl

ace

in a

rac

e.H

ow m

any

cars

are

in

th

e ra

ce?

13

6SDAP3.1

Sol

ve e

ach

pro

ble

m.

1.N

UM

BER

SH

ow m

any

diff

eren

t 2-

digi

t n

um

bers

can

be

form

ed f

rom

th

edi

gits

4,6

,an

d 8?

Ass

um

e n

o n

um

ber

can

be

use

d m

ore

than

on

ce.

6

2.LE

TTER

SH

ow m

any

perm

uta

tion

s ar

e po

ssib

le o

f th

e le

tter

s in

th

e w

ord

NU

MB

ER

S?

7! o

r 5,

040

3.PA

SSEN

GER

ST

her

e ar

e 5

pass

enge

rs i

n a

car

.In

how

man

y w

ays

can

th

epa

ssen

gers

sit

in

th

e 5

pass

enge

r se

ats

of t

he

car?

5! o

r 12

0

4.PA

INTI

NG

SM

r.B

ern

stei

n o

wn

s 14

pai

nti

ngs

,bu

t h

as o

nly

en

ough

wal

lsp

ace

in h

is h

ome

to d

ispl

ay t

hre

e of

th

em a

t an

y on

e ti

me:

one

in t

he

hal

lway

,on

e in

th

e de

n,a

nd

one

in t

he

parl

or.H

ow m

any

way

s ca

n M

r.B

ern

stei

n d

ispl

ay t

hre

e pa

inti

ngs

in

his

hom

e?2,

184

5.D

OG

SH

OW

Mat

eo i

s on

e of

th

e si

x do

g ow

ner

s in

th

e te

rrie

r ca

tego

ry.I

fth

e ow

ner

s ar

e se

lect

ed i

n a

ran

dom

ord

er t

o sh

ow t

hei

r do

gs,h

ow m

any

way

s ca

n t

he

own

ers

show

th

eir

dogs

?6!

or

720

6.TI

ME

Mic

hel

,Jon

ath

an,a

nd

two

of t

hei

r fr

ien

ds e

ach

rid

e th

eir

bike

s to

sch

ool.

If t

hey

hav

e an

equ

ally

-lik

ely

chan

ce o

f ar

rivi

ng

firs

t,w

hat

is

the

prob

abil

ity

that

Jon

ath

an w

ill

arri

ve f

irst

an

d M

ich

el w

ill

arri

vese

con

d?� 11 2�

7.B

IRTH

DA

YG

len

rec

eive

d 6

birt

hda

y ca

rds.

If h

e is

equ

ally

lik

ely

to r

ead

the

card

s in

an

y or

der,

wh

at i

s th

e pr

obab

ilit

y h

e re

ads

the

card

fro

m h

ispa

ren

ts a

nd

the

card

fro

m h

is s

iste

r be

fore

th

e ot

her

car

ds?

CO

DES

For

Exe

rcis

es 8

–10,

use

th

e fo

llow

ing

info

rmat

ion

.A b

ank

giv

esea

ch n

ew c

ust

omer

a 4

-dig

it c

ode

nu

mb

er w

hic

h a

llow

s th

e n

ewcu

stom

er t

o cr

eate

th

eir

own

pas

swor

d.T

he

cod

e n

um

ber

is

assi

gned

ran

dom

ly f

rom

th

e d

igit

s 1,

3,5,

and

7,a

nd

no

dig

it i

s re

pea

ted

.

8.W

hat

is

the

prob

abil

ity

that

th

e co

de n

um

ber

for

a n

ew c

ust

omer

wil

lbe

gin

or

end

wit

h a

7?

�1 2�

9.W

hat

is

the

prob

abil

ity

that

th

e co

de n

um

ber

wil

l n

otco

nta

in a

5?

0

10.

Wh

at i

s th

e pr

obab

ilit

y th

at t

he

code

nu

mbe

r w

ill

star

t w

ith

371

?� 21 4�

1 � 30

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Per

mu

tati

on

s

Cha

pter

930

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-4

6SD

AP

3.1



An

swer

s

Exer

cise

s

Exam

ple

1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

TI-8

3/84

Plu

s A

ctiv

ityP

erm

uta

tio

ns

Cha

pter

933

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–4

pygp

9-4

You

can

use

a g

raph

ing

calc

ulat

or t

o he

lp y

ou f

ind

the

num

ber

of p

erm

utat

ions

.

25 p

eopl

e ar

e au

diti

onin

g fo

r 5

diff

eren

t pa

rts

in a

pl

ay.I

n ho

w m

any

way

s ca

n th

e 5

part

s be

ass

igne

d?

To c

alcu

late

a p

erm

utat

ion,

fin

d th

e to

tal n

umbe

r of

obje

cts

(n)

and

the

num

ber

take

n at

one

tim

e (r

). I

n th

ispr

oble

m, n

�25

. Bec

ause

5 s

tude

nts

are

need

ed, r

�5.

Ent

er:2

5 2

5 6,

375,

600

The

par

ts c

an b

e as

sign

ed in

6,3

75,6

00 d

iffe

rent

way

s.

Fin

d t

he

valu

e of

eac

h p

erm

uta

tion

for

th

e gi

ven

val

ues

of

nan

d r

.

1.n

�5,

r�

220

2.n

�8,

r�

333

63.

n�

9, r

�6

60,4

80

4.n

�6,

r�

230

5.n

�10

, r�

615

1,20

06.

n�

12, r

�4

11,8

80

7.n

�20

, r�

238

08.

n�

15, r

�7

32,4

32,4

009.

n�

18, r

�3

4,89

6

Sol

ve.

10.

Em

ploy

ees

of S

pies

, Inc

., ar

e gi

ven

3-di

git c

ode

num

bers

mad

e up

of

the

digi

ts 1

, 3, 5

, 7, a

nd 9

. How

man

y di

ffer

ent 3

-dig

it c

ode

num

bers

can

be c

reat

ed?

60

11.

How

man

y di

ffer

ent 4

-let

ter

arra

ngem

ents

are

ther

e in

the

lett

ers

A, S

,N

, D, T

, R, a

nd Y

?84

0

12.

Twen

ty s

tude

nts

have

ent

ered

an

art c

onte

st. F

ive

stud

ents

wil

l eac

hre

ceiv

e di

ffer

ent a

war

ds. H

ow m

any

diff

eren

t gro

ups

of 5

stu

dent

sco

uld

be s

elec

ted

to r

ecei

ve a

war

ds?

1,86

0,48

0

EN

TER

MA

TH

Cyc

lic P

erm

uta

tio

ns

1.G

eorg

e,A

lan

,an

d W

illi

am a

re i

n t

he

sam

e m

ath

cla

ss.G

eorg

e h

as f

ive

diff

eren

t sh

irts

an

d w

ears

a d

iffe

ren

t on

e ea

ch d

ay.I

n h

ow m

any

way

sca

n G

eorg

e w

ear

his

fiv

e sh

irts

in

fiv

e da

ys?

5 �

4 �

3 �

2 �

1 �

120

way

s2.

Ala

n h

as t

hre

e di

ffer

ent

shir

ts a

nd

Wil

liam

has

fou

r.W

hic

h o

f th

e th

ree

stu

den

ts,G

eorg

e,A

lan

,or

Wil

liam

,goe

s th

e gr

eate

st n

um

ber

of d

ays

befo

re h

e h

as t

o w

ear

a sh

irt

for

the

seco

nd

tim

e? E

xpla

in.

Geo

rge.

Ala

n c

an w

ear

his

sh

irts

in 3

�2

�1

�6

dif

fere

nt

way

s,an

d W

illia

m c

an w

ear

his

sh

irts

in 4

�3

�2

�1

�24

dif

fere

nt

way

s.G

eorg

e,A

lan

,an

d W

illi

am a

lway

s w

ear

thei

r sh

irts

in

th

e sa

me

orde

r.S

upp

ose

that

Geo

rge’

s 5

shir

ts a

re r

ed,t

an,g

reen

,bla

ck,a

nd

wh

ite.

He

wea

rs h

is s

hir

ts f

ollo

win

g th

is p

atte

rn:

B W

R T

G B

W R

T …

No

mat

ter

wh

ere

Geo

rge

is i

n t

he

patt

ern

,his

fri

ends

can

alw

ays

figu

re o

ut

wh

ich

sh

irt

Geo

rge

wil

l w

ear

nex

t.S

ince

th

ese

perm

uta

tion

s ar

e th

e sa

me

wh

en t

hey

mak

e u

p pa

rt o

f a

cycl

e,th

ey a

re c

alle

d cy

clic

per

mu

tati

ons.

3.A

lan

has

sh

irts

th

at a

re w

hit

e,bl

ack,

and

purp

le.M

ake

an o

rgan

ized

lis

tof

all

th

e di

ffer

ent

perm

uta

tion

s.

WB

P;

BW

P;

PW

B a

nd

WP

B;

BP

W;

PB

W4.

How

man

y di

ffer

ent

way

s ar

e th

ere

for

Ala

n t

o w

ear

his

sh

irts

so

that

his

frie

nds

rec

ogn

ize

diff

eren

t pa

tter

ns?

Exp

lain

.

2 w

ays;

WB

P,B

PW

an

d P

WB

are

cyc

lic p

erm

uta

tio

ns,

and

WP

B,B

WP

an

d P

BW

are

cyc

lic p

erm

uta

tio

ns.

5.W

illi

am h

as a

thle

tic

shir

ts t

hat

are

lab

eled

1,2

,3,a

nd

4.M

ake

anor

gan

ized

lis

t of

all

th

e di

ffer

ent

perm

uta

tion

s.12

34;

2134

;31

24;

4123

1342

;23

41;

3241

;42

3112

43;

2143

;31

42;

4132

1423

;24

13;

3412

;43

1213

24;

2314

;32

14;

4213

1432

;24

31;

3421

;43

21

6.H

ow m

any

diff

eren

t w

ays

are

ther

e fo

r W

illi

am t

o w

ear

his

sh

irts

so

that

his

frie

nds

rec

ogn

ize

diff

eren

t pa

tter

ns?

Exp

lain

.6

way

s;12

34,1

243,

1324

,13

42,1

423

and

143

2 ar

e u

niq

ue

cycl

es.A

ll o

ther

per

mu

tati

on

s ca

nb

e w

ritt

en a

s o

ne

of

thes

e,bu

t in

a d

iffe

ren

t o

rder

.7.

CH

ALL

ENG

EF

or a

ny

give

n n

um

ber

of s

hir

ts,h

ow c

an y

ou d

eter

min

e th

en

um

ber

of w

ays

a pe

rson

cou

ld w

ear

the

shir

ts t

o pr

odu

ce u

niq

ue

patt

ern

s?Ta

ke t

he

fact

ori

al o

f o

ne

less

th

an t

he

nu

mb

er o

fsh

irts

,th

at is

(n

�1)

!.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

932

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-4

6SD

AP

3.1



Exer

cise

s

Jil

l w

as a

sked

by

her

tea

cher

to

choo

se 3

top

ics

from

th

e 8

top

ics

give

n t

o h

er.H

ow m

any

dif

fere

nt

thre

e-to

pic

gr

oup

s co

uld

sh

e ch

oose

?

Th

ere

are

8 · 7

· 6

perm

uta

tion

s of

th

ree-

topi

c gr

oups

ch

osen

fro

m e

igh

t.T

her

e ar

e 3

· 2 ·

1w

ays

to a

rran

ge t

he

grou

ps.

�8�7

�6

� �

�33 66 � �

56

So,

ther

e ar

e 56

dif

fere

nt

thre

e-to

pic

grou

ps.

Tel

l w

het

her

eac

h s

itu

atio

n r

epre

sen

ts a

per

mu

tati

onor

com

bin

ati

on.

Th

en s

olve

th

e p

rob

lem

.

On

a q

uiz

,you

are

all

owed

to

answ

er a

ny

4 ou

t of

th

e 6

qu

esti

ons.

How

man

y w

ays

can

you

ch

oose

th

e q

ues

tion

s?

Th

is i

s a

com

bin

atio

n b

ecau

se t

he

orde

r of

th

e 4

ques

tion

s is

not

im

port

ant.

So,

ther

e ar

e 6

· 5 ·

4 · 3

per

mu

tati

ons

of f

our

ques

tion

s ch

osen

fro

m s

ix.T

her

e ar

e 4

· 3 ·

2 · 1

ord

ers

inw

hic

h t

hes

e qu

esti

ons

can

be

chos

en.

�6�

5 4� !4�

3�

�

�3 26 40 � �

15

So,

ther

e ar

e 15

way

s to

ch

oose

th

e qu

esti

ons.

Fiv

e d

iffe

ren

t ca

rs e

nte

r a

par

kin

g lo

t w

ith

on

ly 3

em

pty

sp

aces

.H

ow m

any

way

s ca

n t

hes

e sp

aces

be

fill

ed?

Th

is i

s a

perm

uta

tion

bec

ause

eac

h a

rran

gem

ent

of t

he

sam

e 3

cars

cou

nts

as

a di

stin

ctar

rran

gem

ent.

So,

ther

e ar

e 5

· 4 ·

3 or

60

way

s th

e sp

aces

can

be

fill

ed.

Tel

l w

het

her

eac

h s

itu

atio

n r

epre

sen

ts a

per

mu

tati

onor

com

bin

ati

on.

Th

en s

olve

th

e p

rob

lem

.

1.H

ow m

any

way

s ca

n 4

peo

ple

be c

hos

en f

rom

a g

rou

p of

11?

com

bin

atio

n;

330

2.H

ow m

any

way

s ca

n 3

peo

ple

sit

in 4

ch

airs

?p

erm

uta

tio

n;

24

3.H

ow m

any

way

s ca

n 2

gol

dfis

h b

e ch

osen

fro

m a

tan

k co

nta

inin

g 15

gol

dfis

h?

com

bin

atio

n;

105

Exam

ple

2

Exam

ple

3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Co

mb

inat

ion

s

Cha

pter

935

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–5

pygp

9-5

An

arra

ngem

ent,

or li

stin

g, o

f ob

ject

s in

whi

ch o

rder

is n

otim

port

ant

is c

alle

d a

com

bin

atio

n.Y

ou c

anfin

d th

e nu

mbe

r of

com

bina

tions

of

obje

cts

by d

ivid

ing

the

num

ber

of p

erm

utat

ions

of

the

entir

e se

t by

the

num

ber

of w

ays

each

sm

alle

r se

t ca

n be

arr

ange

d.

Exam

ple

1

6SDAP3.1

3�

2�

1

4�

3�

2 �

1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

Co

mb

inat

ion

s

Cha

pter

934

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-5

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n a

t th

e to

p o

f p

age

480

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.U

se t

he

firs

t le

tter

of

each

nam

e to

lis

t al

l of

th

e pe

rmu

tati

ons

of

co-c

apta

ins.

How

man

y ar

e th

ere?

JB,J

O,J

D,B

J,B

O,B

D,O

J,O

B,

OD

,DJ,

DB

,DO

;12

2.C

ross

ou

t an

y ar

ran

gem

ent

that

con

tain

s th

e sa

me

lett

ers

as a

not

her

on

ein

th

e li

st.H

ow m

any

are

ther

e n

ow?

6

3.E

xpla

in t

he

diff

eren

ce b

etw

een

th

e tw

o li

sts

abov

e.T

he

list

inE

xerc

ise

1 is

a p

erm

uta

tio

n w

her

e o

rder

is im

po

rtan

t.T

he

list

in E

xerc

ise

2 d

oes

no

t ta

ke o

rder

into

acc

ou

nt.

Rea

d t

he

Less

on

4.H

ow c

an y

ou f

ind

the

nu

mbe

r of

com

bin

atio

ns

of o

bjec

ts i

n a

set

?S

amp

le a

nsw

er:

Div

ide

the

nu

mb

er o

f p

erm

uta

tio

ns

of

the

enti

re s

et b

y th

e n

um

ber

of

way

s ea

ch s

mal

ler

set

can

be

arra

ng

ed.

5.W

hy

mig

ht

it b

e ea

sier

to

calc

ula

te t

he

nu

mbe

r of

com

bin

atio

ns

of a

set

of

obje

cts

usi

ng

a pe

rmu

tati

on r

ath

er t

han

mak

ing

a li

st?

Sam

ple

answ

er:

A li

st c

ou

ld b

e q

uit

e le

ng

thy,

dep

end

ing

on

th

en

um

ber

of

ob

ject

s in

th

e se

t an

d t

he

nu

mb

er o

f th

em b

ein

gch

ose

n.

For

Exe

rcis

es 6

an

d 7

,ref

er t

o E

xam

ple

2 o

n p

age

525

in y

our

text

boo

k.

6.In

th

e di

agra

m,h

ow m

any

poin

ts a

re t

her

e? H

ow m

any

lin

e se

gmen

tsco

nn

ect

to a

ny

one

poin

t?8;

7

7.H

ow d

oes

you

r an

swer

to

Exe

rcis

e 6

abov

e co

rres

pon

d to

Exa

mpl

e 2

inyo

ur

book

?T

her

e ar

e 8

· 7 w

ays

to c

ho

ose

2 p

eop

le.

Rem

emb

er W

hat

Yo

u L

earn

ed8.

Wor

k w

ith

a p

artn

er.T

ake

turn

s th

inki

ng

of s

itu

atio

ns

in w

hic

h a

sele

ctio

n f

rom

a g

rou

p m

ust

be

mad

e,w

her

e or

der

is o

r is

not

im

port

ant.

Tel

l ea

ch o

ther

wh

ich

sit

uat

ion

s ar

e pe

rmu

tati

ons

and

wh

ich

are

com

bin

atio

ns.

Sol

ve e

ach

pro

blem

an

d sh

ow y

our

wor

k.S

ee s

tud

ents

’wo

rk.

6SD

AP

3.1



An

swer

s

Sol

ve e

ach

pro

ble

m.

1.B

ASK

ETB

ALL

In h

ow m

any

way

s ca

n a

coa

ch s

elec

t 5

play

ers

from

a t

eam

of 1

0 pl

ayer

s? 25

2

2.B

OO

KS

In h

ow m

any

way

s ca

n 3

boo

ks b

e se

lect

ed f

rom

a s

hel

f of

25

book

s?

2,30

0

3.C

AFE

TER

IAIn

how

man

y w

ays

can

you

ch

oose

2 s

ide

dish

es f

rom

15

item

s?10

5

4.C

HO

RES

Of

8 h

ouse

hol

d ch

ores

,in

how

man

y w

ays

can

you

do

thre

e-fo

urt

hs

of t

hem

? 2

8

5.EL

DER

LYL

atan

ya v

olu

nte

ers

to b

ake

and

deli

ver

past

ries

to

elde

rly

peop

lein

her

nei

ghbo

rhoo

d.In

how

man

y di

ffer

ent

way

s ca

n L

atan

ya d

eliv

er t

o2

of t

he

6 el

derl

y pe

ople

in

her

nei

ghbo

rhoo

d? 15

6.D

ELI

A d

eli

mak

es p

otat

o,m

acar

oni,

thre

e be

an,C

aesa

r,7-

laye

r,an

dG

reek

sal

ads.

Th

e de

li r

ando

mly

mak

es o

nly

fou

r sa

lads

eac

h d

ay.W

hat

is

the

prob

abil

ity

that

th

e fo

ur

sala

ds m

ade

one

day

are

7-la

yer,

mac

aron

i,G

reek

,an

d po

tato

?� 11 5�

7.A

UTO

GR

APH

SA

spo

rts

mem

orab

ilia

en

thu

sias

t co

llec

ted

auto

grap

hed

bas

ebal

ls f

rom

th

e pl

ayer

s in

th

e ta

ble.

Th

e en

thu

sias

t is

giv

ing

one

auto

grap

hed

ba

seba

ll t

o ea

ch o

f h

is t

hre

e gr

andc

hil

dren

.If

the

base

ball

s ar

e se

lect

ed a

t ra

ndo

m,w

hat

is

the

prob

abil

ity

that

th

e H

ank

Aar

on,A

lex

Rod

riqu

ez,

and

Mic

key

Man

tle

auto

grap

hed

bas

ebal

ls a

re g

iven

to

his

gra

ndc

hil

dren

?� 11 0�

For

Exe

rcis

es 8

–10,

tell

wh

eth

er e

ach

pro

ble

m r

epre

sen

ts a

per

mu

tati

onor

a c

ombi

na

tion

.Th

en s

olve

th

e p

rob

lem

.

8.LO

CK

SIn

how

man

y w

ays

can

th

ree

diff

eren

t n

um

bers

be

sele

cted

fro

m10

nu

mbe

rs t

o op

en a

key

pad

lock

? p

erm

uta

tio

n;

720

9.M

OV

IES

How

man

y w

ays

can

10

DV

Ds

be p

lace

d on

a s

hel

f?p

erm

uta

tio

n;

10!

or

3,62

8,80

0

10.

TRA

NSP

OR

TATI

ON

Eig

ht

peop

le n

eed

tran

spor

tati

on t

o th

e co

nce

rt.H

owm

any

diff

eren

t gr

oups

of

6 pe

ople

can

rid

e w

ith

Mrs

.Joh

nso

n?

com

bin

atio

n;

28

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Co

mb

inat

ion

s

Cha

pter

937

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–5

pygp

9-5

Pla

yer

Cal

Rip

kin

Han

k A

aron

Bar

ry B

onds

Ale

x R

odri

quez

Mic

key

Man

tle

6SD

AP

3.1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eC

om

bin

atio

ns

Cha

pter

936

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-5

Tel

l w

het

her

eac

h s

itu

atio

n r

epre

sen

ts a

per

mu

tati

onor

com

bin

ati

on.

Th

en s

olve

th

e p

rob

lem

.

1.Yo

u a

re a

llow

ed t

o om

it t

wo

out

of 1

2 qu

esti

ons

on a

qu

iz.H

ow m

any

way

s ca

n y

ou s

elec

t th

e qu

esti

ons

to o

mit

?co

mb

inat

ion

;66

2.S

ix s

tude

nts

are

to

be c

hos

en f

rom

a c

lass

of

18 t

o re

pres

ent

the

clas

s at

am

ath

con

test

.How

man

y w

ays

can

th

e si

x st

ude

nts

be

chos

en?

com

bin

atio

n;

18,5

64

3.H

ow m

any

diff

eren

t 5-

digi

t zi

p co

des

are

poss

ible

if

no

digi

ts a

rere

peat

ed?

per

mu

tati

on

;30

,240

4.In

a r

ace

wit

h s

ix r

un

ner

s,h

ow m

any

way

s ca

n t

he

run

ner

s fi

nis

h f

irst

,se

con

d,or

th

ird?

per

mu

tati

on

;12

0

5.H

ow m

any

way

s ca

n t

wo

nam

es b

e ch

osen

fro

m 7

6 in

a r

affl

e if

on

ly o

ne

entr

y pe

r pe

rson

is

allo

wed

?co

mb

inat

ion

;2,

850

6.H

ow m

any

way

s ca

n s

ix s

tude

nts

be

arra

nge

d in

a l

un

ch l

ine?

per

mu

tati

on

;72

0

7.A

fam

ily

has

a b

ike

rack

th

at f

its

seve

n b

ikes

bu

t th

ey o

nly

hav

e fi

vebi

kes.

How

man

y w

ays

can

th

e bi

kes

fit

in t

he

bike

rac

k?p

erm

uta

tio

n;

2,52

0

8.H

ow m

any

way

s ca

n y

ou s

elec

t th

ree

sher

iff

depu

ties

fro

m e

igh

tca

ndi

date

s?co

mb

inat

ion

;56

9.H

ow m

any

way

s ca

n f

our

fin

alis

ts b

e se

lect

ed f

rom

50

con

test

ants

?co

mb

inat

ion

;23

0,30

0

10.

How

man

y 4-

digi

t pi

n n

um

bers

are

ava

ilab

le i

f n

o n

um

ber

is r

epea

ted?

per

mu

tati

on

;5,

040

11.

How

man

y h

ands

hak

es c

an o

ccu

r be

twee

n f

ive

peop

le i

f ev

eryo

ne

shak

esh

ands

?co

mb

inat

ion

;10

6SD

AP

3.1



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

939

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–5

pygp

9-5

Fro

m Im

po

ssib

le t

o C

erta

in E

ven

tsA

pro

babi

lity

is

ofte

n e

xpre

ssed

as

a fr

acti

on.A

s yo

u k

now

,an

eve

nt

that

is

impo

ssib

le i

s gi

ven

a p

roba

bili

ty o

f 0

and

an e

ven

t th

at i

s ce

rtai

n i

s gi

ven

apr

obab

ilit

y of

1.E

ven

ts t

hat

are

nei

ther

im

poss

ible

nor

cer

tain

are

giv

en a

prob

abil

ity

som

ewh

ere

betw

een

0 a

nd

1.T

he

prob

abil

ity

lin

e be

low

sh

ows

rela

tive

pro

babi

liti

es.

Det

erm

ine

the

pro

bab

ilit

y of

an

eve

nt

by

con

sid

erin

g it

s p

lace

on

th

ed

iagr

am a

bov

e.A

nsw

ers

will

var

y.A

ccep

t lo

gic

al r

esp

on

ses.

1.M

edic

al r

esea

rch

wil

l fi

nd

a cu

re f

or a

ll d

isea

ses.

2.T

her

e w

ill

be a

per

son

al c

ompu

ter

in e

ach

hom

e by

th

e ye

ar 2

010.

3.O

ne

day,

peop

le w

ill

live

in

spa

ce o

r u

nde

r th

e se

a.

4.W

ildl

ife

wil

l di

sapp

ear

as E

arth

’s h

um

an p

opu

lati

on i

ncr

ease

s.

5.T

her

e w

ill

be a

fif

ty-f

irst

sta

te i

n t

he

Un

ited

Sta

tes.

6.T

he

sun

wil

l ri

se t

omor

row

mor

nin

g.

7.M

ost

elec

tric

ity

wil

l be

gen

erat

ed b

y n

ucl

ear

pow

er b

y th

e ye

ar 2

010.

8.T

he

fuel

eff

icie

ncy

of

auto

mob

iles

wil

l in

crea

se a

s th

e su

pply

of

gaso

lin

ede

crea

ses.

9.A

stro

nau

ts w

ill

lan

d on

Mar

s.

10.

Th

e pe

rcen

t of

hig

h s

choo

l st

ude

nts

wh

o gr

adu

ate

and

ente

r co

lleg

e w

ill

incr

ease

.

11.

Glo

bal

war

min

g pr

oble

ms

wil

l be

sol

ved.

12.

All

peo

ple

in t

he

Un

ited

Sta

tes

wil

l ex

erci

se r

egu

larl

y w

ith

in t

he

nea

rfu

ture

.

equa

lly li

kely

pret

tylik

ely

1

certa

inno

t so

likel

y

1 41 2

3 40

impo

ssib

le

6SD

AP

3.1

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Co

mb

inat

ion

s

Cha

pter

938

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-5

1.SN

AC

KS

A v

endi

ng

mac

hin

e ca

n d

ispl

aysi

x sn

acks

.If

ther

e ar

e ei

ght

diff

eren

tki

nds

of

snac

ks a

vail

able

,how

man

ydi

ffer

ent

grou

ps o

f si

x di

ffer

ent

snac

ksca

n b

e di

spla

yed?

28

2.M

USI

CE

ach

mon

th,J

ose

purc

has

es t

wo

CD

s fr

om a

sel

ecti

on o

f 20

bes

tsel

lin

gC

Ds.

How

man

y di

ffer

ent

pair

s of

CD

sca

n J

ose

choo

se i

f h

e ch

oose

s tw

odi

ffer

ent

CD

s?19

0

3.TE

STS

On

a m

ath

tes

t,yo

u c

an c

hoo

sean

y 20

ou

t of

23

ques

tion

s.H

ow m

any

diff

eren

t gr

oups

of

20 q

ues

tion

s ca

nyo

u c

hoo

se?

1,77

1

4.R

ESTA

UR

AN

TST

he

din

ner

spe

cial

at

alo

cal

pizz

a pa

rlor

giv

es y

ou t

he

choi

ceof

tw

o to

ppin

gs f

rom

a s

elec

tion

of

six

topp

ings

.How

man

y di

ffer

ent

choi

ces

are

poss

ible

if

two

diff

eren

t to

ppin

gsar

e ch

osen

?15

5.TE

STIN

GIn

a s

cien

ce f

air

expe

rim

ent,

two

un

its

are

sele

cted

for

tes

tin

g fr

omev

ery

500

un

its

prod

uce

d.H

ow m

any

way

s ca

n t

hes

e tw

o u

nit

s be

sel

ecte

d?12

4,75

0

6.M

EETI

NG

SL

inda

’s t

each

er d

ivid

ed t

he

clas

s in

to g

rou

ps o

f fi

ve a

nd

requ

ired

each

mem

ber

of a

gro

up

to m

eet

wit

hev

ery

oth

er m

embe

r of

th

at g

rou

p.H

owm

any

mee

tin

gs w

ill

each

gro

up

hav

e?10

7.B

ASE

BA

LLA

bas

ebal

l co

ach

has

13

play

ers

to f

ill

nin

e po

siti

ons.

How

man

ydi

ffer

ent

team

s co

uld

he

put

toge

ther

?71

5

8.G

EOM

ETRY

Ten

poi

nts

are

mar

ked

on a

circ

le.H

ow m

any

diff

eren

t tr

ian

gles

can

be

draw

n b

etw

een

an

y th

ree

poin

ts?

120

6SD

AP

3.1



An

swer

s

Exer

cise

s

Exam

ple

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

941

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–6

pygp

9-6

CLO

THIN

GR

icar

do

has

tw

o sh

irts

an

d t

hre

e p

airs

of

pan

ts t

o ch

ose

from

for

his

ou

tfit

to

wea

r on

th

e fi

rst

day

of

sch

ool.

How

man

yd

iffe

ren

t ou

tfit

s ca

n h

e m

ake

by

wea

rin

g on

e sh

irt

and

on

e p

air

ofp

ants

?

By

actin

g ou

t a

prob

lem

, yo

u ar

e ab

le t

o se

e al

l pos

sibl

e so

lutio

ns t

o th

e pr

oble

m b

eing

pos

ed.

Exp

lore

We

know

th

at h

e h

as t

wo

shir

ts a

nd

thre

e pa

irs

of p

ants

to

choo

se f

rom

.We

can

use

a c

oin

for

th

e sh

irts

an

d an

equ

ally

div

ided

spi

nn

er l

abel

ed f

or t

he

pan

ts.

Pla

nL

et’s

mak

e a

list

sh

owin

g al

l po

ssib

le o

utc

omes

of

toss

ing

a co

in a

nd

then

spin

nin

g a

spin

ner

.

Sol

veH

�H

eads

T �

Tai

lsS

pin

ner

�1,

2,3

Th

ere

are

six

poss

ible

ou

tcom

es o

f fl

ippi

ng

a co

in a

nd

spin

nin

g a

spin

ner

.S

o,th

ere

are

6 di

ffer

ent

poss

ible

ou

tfit

s th

at R

icar

do c

an w

ear

for

the

firs

t da

yof

sch

ool.

Ch

eck

Fli

ppin

g a

coin

has

tw

o ou

tcom

es a

nd

ther

e ar

e tw

o sh

irts

.S

pin

nin

g a

thre

e-se

ctio

n s

pin

ner

has

th

ree

outc

omes

an

d th

ere

are

thre

e pa

irs

of p

ants

.T

her

efor

e,th

e so

luti

on o

f 6

diff

eren

t ou

tcom

es w

ith

a c

oin

an

d sp

inn

erre

pres

ent

the

6 po

ssib

le o

utf

it o

utc

omes

for

Ric

ardo

.

Fli

p a

Coi

nS

pin

a S

pin

ner

H1

H2

H3

T1

T2

T3

1.SC

IEN

CE

FAIR

Th

ere

are

4 st

ude

nts

wit

h p

roje

cts

to p

rese

nt

at t

he

sch

ool

scie

nce

fai

r.H

ow m

any

diff

eren

t w

ays

can

th

ese

4 pr

ojec

ts b

e di

spla

yed

on f

our

tabl

es i

n a

row

?24

way

s

2.G

END

ERD

eter

min

e w

het

her

fli

ppin

g a

coin

is

a go

od w

ay t

o pr

edic

t th

ege

nde

r of

th

e n

ext

5 ba

bies

bor

n a

t G

ener

al H

ospi

tal.

Just

ify

you

ran

swer

.N

o;

ther

e is

on

ly o

ne

scen

ario

in w

hic

h t

he

pre

dic

tio

n is

co

rrec

t.

3.O

LYM

PIC

SF

our

run

ner

s ar

e en

tere

d in

th

e fi

rst

hu

rdle

s h

eat

of t

wel

veh

eats

at

the

Oly

mpi

cs.

Th

e fi

rst

two

mov

e on

to

the

nex

t ro

un

d.A

ssu

min

g n

o ti

es,h

ow m

any

diff

eren

t w

ays

can

th

e fo

ur

run

ner

s co

me

infi

rst

and

seco

nd

plac

e?12

way

s

6SD

AP

3.2,

6S

DA

P2.

4St

udy

Guid

e an

d In

terv

entio

nP

rob

lem

-So

lvin

g In

vest

igat

ion

:A

ct It

Ou

t

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

TI-8

3/84

Plu

s A

ctiv

ityC

om

bin

atio

ns

Cha

pter

940

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-5

A g

raph

ing

calc

ulat

or c

an b

e us

ed t

o so

lve

prob

lem

s in

volv

ing

com

bina

tion

s.O

n th

e T

I-83

/84

Plu

s,th

e co

mbi

nati

on f

unct

ion

can

be f

ound

in t

he M

ATH

(PRB

)men

u.

How

man

y w

ays

can

2 pe

ople

be

chos

en f

rom

a

grou

p of

10

peop

le?

Sin

ce o

rder

doe

s no

t mat

ter,

this

is a

com

bina

tion

.

Ent

er:

10

3 2

45

So,

the

num

ber

of w

ays

2 pe

ople

can

be

chos

en f

rom

a g

roup

of

10

peop

le is

45.

How

man

y 5-

card

han

ds c

an b

e ch

osen

fro

m a

de

ck o

f 52

car

ds?

Sin

ce o

rder

doe

s no

t mat

ter,

this

is a

com

bina

tion

.

Ent

er:

52

3 5

2,59

8,96

0

So,

the

num

ber

of 5

-car

d ha

nds

that

can

be

chos

en f

rom

a 5

2-ca

rd d

eck

is2,

598,

960.

Sol

ve e

ach

pro

ble

m.

1.H

ow m

any

grou

ps o

f 3

peop

le c

an b

e ch

osen

fro

m a

gro

up o

f 5

peop

le?

10

2.H

ow m

any

grou

ps o

f 4

peop

le c

an b

e ch

osen

fro

m a

gro

up o

f 8

peop

le?

70

3.H

ow m

any

grou

ps o

f 10

peo

ple

can

be c

hose

n fr

om a

gro

up o

f 20

peo

ple?

184,

756

4.H

ow m

any

grou

ps o

f 2

peop

le c

an b

e ch

osen

fro

m a

gro

up o

f 12

peo

ple?

66

5.H

ow m

any

grou

ps o

f 8

peop

le c

an b

e ch

osen

fro

m a

gro

up o

f 9

peop

le?

9

6.H

ow m

any

2-to

ppin

g pi

zzas

can

be

mad

e fr

om a

piz

za r

esta

uran

t of

feri

ng 6

dif

fere

nt

topp

ings

?15

7.H

ow m

any

3-to

ppin

g pi

zzas

can

be

mad

e fr

om a

piz

za r

esta

uran

t of

feri

ng 1

0 di

ffer

ent

topp

ings

?12

0

8.H

ow m

any

7-ca

rd h

ands

can

be

chos

en f

rom

a d

eck

of 5

2 ca

rds?

133,

784,

560

9.H

ow m

any

4-ca

rd h

ands

can

be

chos

en f

rom

a d

eck

of 5

2 ca

rds?

270,

725

10.

How

man

y tw

o-to

ppin

g su

ndae

s ca

n be

mad

e fr

om a

n ic

e cr

eam

sho

p of

feri

ng 9

dif

fere

nt

topp

ings

?36

EN

TER

MA

TH

EN

TER

MA

TH

Exam

ple

1

Exam

ple

2



Sele

ct t

he

Op

erat

ion

Mix

ed P

rob

lem

Sol

vin

g

For

Exe

rcis

es 1

an

d 2

,use

th

e ac

t it

ou

tst

rate

gy.

1.PO

P Q

UIZ

Use

th

e in

form

atio

n i

n t

he

tabl

e to

det

erm

ine

wh

eth

er t

ossi

ng

an

icke

l an

d a

dim

e is

a g

ood

way

to

answ

er a

5-q

ues

tion

mu

ltip

le-c

hoi

cequ

iz i

f ea

ch q

ues

tion

has

an

swer

ch

oice

sA

,B,C

,an

d D

.Ju

stif

y yo

ur

answ

er.

No

;S

amp

le a

nsw

er:T

he

exp

erim

ent

pro

du

ces

on

ly

1-2

corr

ect

answ

ers,

so

toss

ing

a n

icke

l an

d a

dim

e is

no

t a

go

od

way

to

an

swer

a

5-q

ues

tio

n m

ult

iple

-ch

oic

e q

uiz

.

2.B

OW

LIN

GB

ill,

Lu

cas,

Car

men

,an

dD

ena

go b

owli

ng

ever

y w

eek.

Wh

enor

dere

d fr

om h

igh

est

to l

owes

t,h

owm

any

way

s ca

n t

hei

r sc

ores

be

arra

nge

dif

Lu

cas

is n

ever

fir

st a

nd

Car

men

alw

ays

beat

s B

ill?

9

Use

an

y st

rate

gy t

o so

lve

Exe

rcis

es 3

and

4.S

ome

stra

tegi

es a

re s

how

n b

elow

.

3.B

OO

KS

Wh

at i

s th

e pr

obab

ilit

y of

fiv

ebo

oks

bein

g pl

aced

in

alp

hab

etic

al o

rder

of t

hei

r ti

tles

if

ran

dom

ly p

ut

on a

boo

ksh

elf?

4.N

UM

BER

TH

EORY

Th

e su

m o

f a

2-di

git

nu

mbe

r an

d th

e 2-

digi

t n

um

ber

wh

enth

e di

gits

are

rev

erse

d is

77.

If t

he

diff

eren

ce o

f th

e sa

me

two

nu

mbe

rs i

s45

,wh

at a

re t

he

two

2-di

git

nu

mbe

rs?

Th

e n

um

ber

s ar

e 61

an

d 1

6.

For

Exe

rcis

es 5

an

d 6

,sel

ect

the

app

rop

riat

e op

erat

ion

(s)

to s

olve

th

ep

rob

lem

s.J

ust

ify

you

r so

luti

on(s

) an

dso

lve

the

pro

ble

m.

5.B

ASE

BA

LLIn

on

e ga

me,

Raf

ael

was

up

toba

t 3

tim

es a

nd

mad

e 2

hit

s.In

an

oth

erga

me,

he

was

up

to b

at 5

tim

es w

ith

no

hit

s.W

hat

per

cen

t of

th

e ti

mes

at

bat

did

Raf

ael

mak

e a

hit

?A

dd

itio

n a

nd

div

isio

n;

2�

0�

2;3

�5

�8;

�2 8��

�1 4��

25%

6.R

ESTA

UR

AN

TA

res

tau

ran

t of

fers

th

epo

ssib

ilit

y of

168

th

ree-

cou

rse

din

ner

s.E

ach

din

ner

has

an

app

etiz

er,a

n e

ntr

ée,

and

a de

sser

t.If

th

e n

um

ber

ofap

peti

zers

dec

reas

es f

rom

7 t

o 5,

fin

dh

ow m

any

few

er p

ossi

ble

thre

e-co

urs

edi

nn

ers

the

rest

aura

nt

offe

rs.

Div

isio

n,m

ult

iplic

atio

n,a

nd

sub

trac

tio

n;

168

�7

�24

;24

�5

�12

0;16

8�

120

�48

;48

few

er p

oss

ible

din

ner

s

1� 12

0

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

943

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–6

pygp

9-6 P

RO

BL

EM

-SO

LVIN

G S

TR

AT

EG

IES

•U

se t

he fo

ur-s

tep

plan

.

•D

raw

a d

iagr

am.

•D

eter

min

e re

ason

able

ans

wer

s.

•A

ct it

out

.

Nic

kel

Dim

eA

nsw

er C

hoi

ceH

HA

HT

BT

HC

TT

D

6SD

AP

3.2,

6S

DA

P2.

4Pr

actic

eP

rob

lem

-So

lvin

g In

vest

igat

ion

:A

ct It

Ou

tU

se t

he

act

it o

ut

stra

tegy

to

solv

e.

1.SC

HO

OL

Det

erm

ine

wh

eth

er r

olli

ng

a 6-

side

d n

um

ber

cube

is

a go

od w

ayto

an

swer

a 2

0-qu

esti

on m

ult

iple

-ch

oice

tes

t if

th

ere

are

six

choi

ces

for

each

qu

esti

on.J

ust

ify

you

r an

swer

.N

o,y

ou

on

ly h

ave

a 1

in 6

chan

ce o

f g

etti

ng

th

e co

rrec

t an

swer

.

2.G

YM

NA

STIC

SF

ive

gym

nas

ts a

re e

nte

red

in a

com

peti

tion

.Ass

um

ing

that

ther

e ar

e n

o ti

es,h

ow m

any

way

s ca

n f

irst

,sec

ond,

and

thir

d pl

aces

be

awar

ded?

60

3.LU

NC

HH

ow m

any

way

s ca

n 3

fri

ends

sit

tog

eth

er i

n t

hre

e se

ats

at l

un

ch?

6

4.SC

HED

ULE

How

man

y di

ffer

ent

sch

edu

les

can

Sh

eila

cre

ate

if s

he

has

to

take

En

glis

h,m

ath

,sci

ence

,soc

ial

stu

dies

,an

d ar

t n

ext

sem

este

r.A

ssu

me

that

th

ere

is o

nly

on

e lu

nch

per

iod

avai

labl

e.12

0

5.B

AN

D C

ON

CER

TST

he

ban

d is

hav

ing

a h

olid

ay c

once

rt.I

n t

he

firs

t ro

w,

the

firs

t tr

um

pet

is a

lway

s fu

rth

est

to t

he

righ

t an

d th

e fi

rst

trom

bon

e is

alw

ays

the

furt

hes

t to

th

e le

ft.H

ow m

any

way

s ar

e th

ere

to a

rran

ge t

he

oth

er 4

peo

ple

wh

o n

eed

to s

it i

n t

he

fron

t? 24

6.TE

AM

SM

r.D

is

pick

ing

team

s fo

r vo

lley

ball

in

gym

by

hav

ing

the

stu

den

ts c

oun

t of

f by

2’s

.Th

e 1’

s w

ill

be o

n o

ne

team

an

d th

e 2’

s on

th

eot

her

.Wou

ld f

lipp

ing

a co

in w

ould

wor

k ju

st a

s w

ell

to p

ick

the

team

s?Ju

stif

y yo

ur

answ

er.

Ap

pro

xim

atel

y,ye

s;b

ecau

se t

he

pro

bab

ility

of

get

tin

g e

ith

er h

ead

s o

r ta

ils is

�1 2� ,th

e sa

me

asg

etti

ng

a o

ne

or

a tw

o.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

942

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-6

6SD

AP

3.2,

6S

DA

P2.

4Sk

ills

Prac

tice

Pro

ble

m-S

olv

ing

Inve

stig

atio

n:

Act

it O

ut



An

swer

s

Get

Rea

dy

for

the

Less

on

Com

ple

te t

he

Min

i L

ab a

t th

e to

p o

f p

age

486

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.C

ompa

re t

he

nu

mbe

r of

tim

es y

ou e

xpec

ted

to r

oll

a su

m o

f 7

wit

h t

he

nu

mbe

r of

tim

es y

ou a

ctu

ally

roll

ed a

su

m o

f 7.

Th

en c

ompa

re y

our

resu

ltto

th

e re

sult

s of

oth

er g

rou

ps.

See

stu

den

ts’w

ork

.

2.W

rite

th

e pr

obab

ilit

y of

rol

lin

g a

sum

of

7 ou

t of

36

roll

s u

sin

g th

en

um

ber

of t

imes

you

exp

ecte

dto

rol

l a

7 fr

om S

tep

1.T

hen

wri

te t

he

prob

abil

ity

of r

olli

ng

a su

m o

f 7

out

of 3

6 ro

lls

usi

ng

the

nu

mbe

r of

tim

esyo

u a

ctu

ally

roll

ed a

su

m o

f 7

from

Ste

p 2.

See

stu

den

ts’w

ork

.

Rea

d t

he

Less

on

3.L

ook

up

the

wor

d ex

peri

men

tal

in a

dic

tion

ary.

Wri

te t

he

mea

nin

g fo

r th

ew

ord

as u

sed

in t

he

less

on.

Sam

ple

an

swer

:b

ased

on

exp

erie

nce

rat

her

th

an o

n t

heo

ry

4.H

ow d

oes

theo

reti

cal

prob

abil

ity

diff

er f

rom

exp

erim

enta

l pr

obab

ilit

y?S

amp

le a

nsw

er:T

heo

reti

cal p

rob

abili

ty is

th

e ex

pec

ted

pro

bab

ility

of

an e

ven

t h

app

enin

g.E

xper

imen

tal p

rob

abili

tyis

bas

ed o

n s

om

eth

ing

yo

u a

ctu

ally

try

(fo

r ex

amp

le,a

nex

per

imen

t o

r g

ame)

.5.

Com

plet

e th

e se

nte

nce

:Exp

erim

enta

l pr

obab

ilit

y ca

n b

e ba

sed

onp

ast

per

form

ance

san

d ca

n b

e u

sed

to m

ake

pred

icti

ons

abou

t fu

ture

even

ts.

Rem

emb

er W

hat

Yo

u L

earn

ed6.

Wor

k w

ith

a p

artn

er.D

esig

n a

n e

xper

imen

t th

at y

ou c

an u

se t

o ex

pres

sth

e ex

peri

men

tal

prob

abil

ity

of a

n e

ven

t.C

ompa

re y

our

fin

din

gs w

ith

thos

e of

oth

ers

in y

our

clas

s.S

ee s

tud

ents

’wo

rk.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

945

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

pygp

9-7

Lesson 9–7

6SD

AP

3.2

Less

on R

eadi

ng G

uide

T

heo

reti

cal a

nd

Exp

erim

enta

l Pro

bab

ility

Sol

ve e

ach

pro

ble

m u

sin

g an

y st

rate

gy y

ou h

ave

lear

ned

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

944

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-6

3.B

ASE

BA

LLT

hir

ty-t

wo

team

s ar

e pl

ayin

gin

th

e ch

ampi

onsh

ip.I

f a

team

is

elim

inat

ed o

nce

it

lose

s,h

ow m

any

tota

l ga

mes

wil

l be

pla

yed

in t

he

cham

pion

ship

?31

4.G

EOM

ETRY

Fin

d th

e n

ext

two

term

s in

the

sequ

ence

.

5.PO

OL

REN

TAL

Th

e ta

ble

belo

w s

how

sh

ow m

uch

For

d M

iddl

e S

choo

l w

asch

arge

d to

ren

t th

e po

ol f

or a

par

tyba

sed

on t

he

nu

mbe

r of

hou

rs i

t w

asre

nte

d.P

redi

ct t

he

cost

for

5 h

ours

.$6

00

6.G

EOM

ETRY

Use

th

e fo

rmu

la D

�rt

wh

ere

Dis

th

e di

stan

ce,r

is t

he

rate

,an

d t

is t

he

tim

e to

det

erm

ine

how

far

Aly

ssa

drov

e if

sh

e dr

ove

55 m

iles

per

hou

r fo

r 4

hou

rs.

220

mile

s

7.SC

HO

OL

ELEC

TIO

NS

How

man

y w

ays

can

a p

resi

den

t,vi

ce p

resi

den

t,se

cret

ary

and

trea

sure

r be

ele

cted

fr

om a

ch

oice

of

6 st

ude

nts

?36

0

8.SH

OPP

ING

Mor

ty b

ough

t sk

is.T

he

skis

cost

$21

5 an

d h

e go

t $3

5 in

ch

ange

.H

ow m

uch

did

Mor

ty p

ay w

ith

?$2

50

# of

hou

rsC

ost

1$1

201.

5$1

802

$240

2.5

$300

An

swer

:

1.PO

LLS

Ou

t of

200

peo

ple,

32%

sai

d th

atth

eir

favo

rite

an

imal

was

a c

at a

nd

44%

sai

d th

at t

hei

r fa

vori

te a

nim

al w

asa

dog.

How

man

y m

ore

peop

le c

hos

edo

g th

an c

at?

24

2.PE

AC

HES

Roi

is

pick

ing

peac

hes

He

nee

ds a

tot

al o

f 3�

1 2�bu

shel

s of

pea

ches

.

If h

e h

as a

lrea

dy p

icke

d 3

bush

els,

how

man

y m

ore

does

he

nee

d to

pic

k?B

A2

bush

els

C3�

1 2�bu

shel

s

B�1 2�

bush

elD

3 bu

shel

s

6SD

AP

3.2,

6S

DA

P2.

4W

ord

Prob

lem

Pra

ctic

eP

rob

lem

-So

lvin

g In

vest

igat

ion

:A

ct It

Ou

t



For

Exe

rcis

es 1

–5,a

nu

mb

er c

ub

e is

rol

led

50

tim

es a

nd

th

e re

sult

sar

e sh

own

in

th

e gr

aph

bel

ow.

1.F

ind

the

expe

rim

enta

l pr

obab

ilit

y of

rol

lin

g a

2.� 24 5�

2.W

hat

is

the

theo

reti

cal

prob

abil

ity

of r

olli

ng

a 2?

�1 6�

3.F

ind

the

expe

rim

enta

l pr

obab

ilit

y of

not

roll

ing

a 2.

�2 21 5�

4.W

hat

is

the

theo

reti

cal

prob

abil

ity

of n

otro

llin

g a

2?�5 6�

5.F

ind

the

expe

rim

enta

l pr

obab

ilit

y of

rol

lin

g a

1.�1 5�

For

Exe

rcis

es 6

–9,u

se t

he

resu

lts

of t

he

surv

ey a

t th

e ri

ght.

6.W

hat

is

the

prob

abil

ity

that

a p

erso

n’s

fa

vori

te s

easo

n i

s fa

ll?

Wri

te t

he

prob

abil

ity

as a

fra

ctio

n.

�1 4�

7.O

ut

of 3

00 p

eopl

e,h

ow m

any

wou

ld y

ou

expe

ct t

o sa

y th

at f

all

is t

hei

r fa

vori

te s

easo

n?

75

8.O

ut

of 2

0 pe

ople

,how

man

y w

ould

you

exp

ect

to s

ay t

hat

th

ey l

ike

all

the

seas

ons?

2

9.O

ut

of 6

50 p

eopl

e,h

ow m

any

mor

e w

ould

you

exp

ect

to s

ay t

hat

th

ey l

ike

sum

mer

th

an s

ay t

hat

th

ey l

ike

win

ter?

169

Sprin

g

Sum

mer

Fall

Win

ter

Non

e, I

like

them

all

13%

39%

25%

13%

10%

Wha

t is

your

favo

rite

seas

on o

f the

yea

r?

63

21

81012 4614 02

Number of Rolls

54

108

6

9

5

12

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

947

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–7

pygp

9-7

6SD

AP

3.2

Skill

s Pr

actic

eT

heo

reti

cal a

nd

Exp

erim

enta

l Pro

bab

ility

Exer

cise

s

Th

e gr

aph

sh

ows

the

resu

lts

of a

n

exp

erim

ent

in w

hic

h a

nu

mb

ercu

be

was

rol

led

100

tim

es.F

ind

th

e ex

per

imen

tal

pro

bab

ilit

y of

rol

lin

g a

3 fo

r th

is e

xper

imen

t.

P(3

) �

� � 11 06 0�

or � 24 5�

Th

e ex

peri

men

tal

prob

abil

ity

of r

olli

ng

a 3

is � 24 5�

,wh

ich

is

clos

e to

its

th

eore

tica

l

prob

abil

ityo

f �1 6�.

In a

tel

eph

one

pol

l,22

5 p

eop

le w

ere

ask

ed

for

wh

om t

hey

pla

nn

ed t

o vo

te i

n t

he

race

fo

r m

ayor

.Wh

at i

s th

e ex

per

imen

tal

pro

bab

ilit

y of

J

uar

ez b

ein

g el

ecte

d?

Of

the

225

peop

le p

olle

d,75

pla

nn

ed t

o vo

te f

or J

uar

ez.

So,

the

expe

rim

enta

l pr

obab

ilit

y is

� 27 25 5�or

�1 3�.

Su

pp

ose

5,70

0 p

eop

le v

ote

in t

he

elec

tion

.H

ow m

any

can

be

exp

ecte

d t

o vo

te f

or J

uar

ez?

�1 3��

5,70

0 �

1,9

00

Abo

ut

1,90

0 w

ill

vote

for

Ju

arez

.

For

Exe

rcis

es 1

–3,u

se t

he

grap

h o

f a

surv

ey o

f 15

0 st

ud

ents

ask

ed w

het

her

th

ey p

refe

r ca

ts o

r d

ogs.

1.W

hat

is

the

prob

abil

ity

of a

stu

den

t pr

efer

rin

g do

gs?

�2 22 5�

2.S

upp

ose

100

stu

den

ts w

ere

surv

eyed

.How

man

y ca

n b

e ex

pect

ed t

o pr

efer

dog

s?88

3.S

upp

ose

300

stu

den

ts w

ere

surv

eyed

.How

man

y ca

n b

e ex

pect

ed t

o pr

efer

cat

s?36

Dog

sC

ats

6080100 40 020120

140

Number of Students

18

132

nu

mbe

r of

tim

es 3

occ

urs

��

��

nu

mbe

r of

pos

sibl

e ou

tcom

es6

32

1

20 101525 05

Number of Rolls

54

1413

1619

2117

Num

ber S

how

ing

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

946

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-7

Exp

erim

enta

l pro

bab

ility

is fo

und

usin

g fr

eque

ncie

s ob

tain

ed in

an

expe

rimen

t or

gam

e.T

heo

reti

cal

pro

bab

ility

is t

he e

xpec

ted

prob

abili

ty o

f an

eve

nt o

ccur

ring.

Can

did

ate

Nu

mb

er o

fP

eop

leJu

arez

75D

avis

67A

bram

son

83

Exam

ple

1

Exam

ple

2

Exam

ple

3

6SD

AP

3.2

Stud

y Gu

ide

and

Inte

rven

tion

Th

eore

tica

l an

d E

xper

imen

tal P

rob

abili

ty



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

949

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–7

pygp

9-7

HO

BB

IES

For

Exe

rcis

es 1

–3,u

se t

he

WIN

TER

AC

TIV

ITIE

SF

or E

xerc

ises

5 a

nd

6,

grap

h o

f a

surv

ey o

f 24

sev

enth

gra

de

use

th

e gr

aph

of

a su

rvey

wit

h 1

04st

ud

ents

ask

ed t

o n

ame

thei

r fa

vori

te

resp

onse

s in

wh

ich

res

pon

den

ts w

ere

hob

by

.as

ked

ab

out

thei

r fa

vori

te w

inte

r ac

tivi

ties

.

1020

3040

5060

700

Bui

ldin

g a

snow

man

Snow

boar

ding

/ski

ing

Sled

ding

Wha

t is

your

favo

rite

win

ter

activ

ity?

1469

21 Resp

onde

nts

24

68

1012

140

Sing

ing

Han

ging

with

frie

nds

Bui

ldin

g th

ings

Bik

e rid

ing

T.V.

Com

pute

rRo

ller

skat

ing

Spor

tsWha

t is

your

favo

rite

hob

by?

13

12

3 3 38

Num

ber o

f Stu

dent

s

1.W

hat

is

the

prob

abil

ity

that

a s

tude

nt’s

favo

rite

hob

by i

s ro

ller

ska

tin

g?

�1 8�

2.S

upp

ose

200

seve

nth

gra

de s

tude

nts

wer

e su

rvey

ed.H

ow m

any

can

be

expe

cted

to

say

that

rol

ler

skat

ing

isth

eir

favo

rite

hob

by?

25

3.S

upp

ose

60 s

even

th g

rade

stu

den

tsw

ere

surv

eyed

.How

man

y ca

n b

eex

pect

ed t

o sa

y th

at b

ike

ridi

ng

is t

hei

rfa

vori

te h

obby

?5

4.M

AR

BLE

SA

bag

con

tain

s 5

blu

e,4

red,

9 w

hit

e,an

d 6

gree

n m

arbl

es.I

f a

mar

ble

is d

raw

n a

t ra

ndo

m a

nd

repl

aced

100

tim

es,h

ow m

any

tim

esw

ould

you

exp

ect

to d

raw

a g

reen

mar

ble?

25

5.W

hat

is

the

prob

abil

ity

that

som

eon

e’s

favo

rite

win

ter

acti

vity

is

buil

din

g a

snow

man

? W

rite

th

e pr

obab

ilit

y as

afr

acti

on.

� 57 2�

6.If

500

peo

ple

had

res

pon

ded,

how

man

yw

ould

hav

e be

en e

xpec

ted

to l

ist

sled

din

g as

th

eir

favo

rite

win

ter

acti

vity

? R

oun

d to

th

e n

eare

st w

hol

epe

rson

.10

1

6SD

AP

3.2

Wor

d Pr

oble

m P

ract

ice

Th

eore

tica

l an

d E

xper

imen

tal P

rob

abili

tyF

or E

xerc

ises

1–4

,a n

um

ber

cu

be

is r

olle

d 2

4 ti

mes

an

d l

and

s on

2fo

ur

tim

es a

nd

on

6 t

hre

e ti

mes

.

1.F

ind

the

expe

rim

enta

l pr

obab

ilit

y of

lan

din

g on

a 2

.�1 6�

2.F

ind

the

expe

rim

enta

l pr

obab

ilit

y of

not

lan

din

g on

a 6

.�7 8�

3.C

ompa

re t

he

expe

rim

enta

l pr

obab

ilit

y yo

u f

oun

d in

Exe

rcis

e 1

to i

tsth

eore

tica

l pr

obab

ilit

y.T

he

theo

reti

cal p

rob

abili

ty o

f la

nd

ing

on

a 2,

�1 6� ,is

th

e sa

me

as t

he

exp

erim

enta

l pro

bab

ility

.

4.C

ompa

re t

he

expe

rim

enta

l pr

obab

ilit

y yo

u f

oun

d in

Exe

rcis

e 2

to i

tsth

eore

tica

l pr

obab

ilit

y.T

he

theo

reti

cal p

rob

abili

ty o

f n

ot

lan

din

g

on

a 6

,�5 6�

,is

fair

ly c

lose

to

th

e ex

per

imen

tal p

rob

abili

ty.

ENTE

RTA

INM

ENT

For

Exe

rcis

es 5

–7,u

se t

he

resu

lts

of t

he

surv

ey

in t

he

tab

le s

how

n.

5.W

hat

is

the

prob

abil

ity

that

som

eon

ein

th

e su

rvey

con

side

red

read

ing

book

s or

su

rfin

g th

e In

tern

et a

s th

ebe

st e

nte

rtai

nm

ent

valu

e? W

rite

th

epr

obab

ilit

y as

a f

ract

ion

.� 13 01 0�

6.O

ut

of 5

00 p

eopl

e su

rvey

ed,h

ow m

any

wou

ld y

ou e

xpec

t co

nsi

dere

d re

adin

gbo

oks

or s

urf

ing

the

Inte

rnet

as

the

best

en

tert

ain

men

t va

lue?

155

7.O

ut

of 3

00 p

eopl

e su

rvey

ed,i

s it

reas

onab

le t

o ex

pect

th

at 3

0co

nsi

dere

d w

atch

ing

tele

visi

on a

s th

ebe

st e

nte

rtai

nm

ent

valu

e? W

hy

or w

hy

not

? N

o;

1% o

f 30

0 =

3,n

ot

30.

For

Exe

rcis

es 8

–10,

a sp

inn

er m

ark

ed w

ith

fou

r se

ctio

ns

blu

e,gr

een

,ye

llow

,an

d r

ed w

as s

pu

n 1

00 t

imes

.Th

e re

sult

s ar

e sh

own

in

th

e ta

ble

.

8.F

ind

the

expe

rim

enta

l pr

obab

ilit

y of

lan

din

g on

gre

en.

� 11 0�

9.F

ind

the

expe

rim

enta

l pr

obab

ilit

y of

lan

din

g on

red

.�1 27 5�

10.

If t

he

spin

ner

is

spu

n 5

0 m

ore

tim

es,

how

man

y of

th

ese

tim

es w

ould

you

ex

pect

th

e po

inte

r to

lan

d on

blu

e?7

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Cha

pter

948

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-7

Sec

tion

Fre

qu

ency

Blu

e14

Gre

en10

Yell

ow8

Red

68

Bes

t E

nte

rtai

nm

ent

Val

ue

Typ

e of

En

tert

ain

men

tP

erce

nt

Pla

yin

g In

tera

ctiv

e G

ames

48%

Rea

din

g B

ooks

22%

Ren

tin

g M

ovie

s10

%G

oin

g to

Mov

ie T

hea

ters

10%

Su

rfin

g th

e In

tern

et9%

Wat

chin

g T

elev

isio

n1%

6SD

AP

3.2

Prac

tice

Th

eore

tica

l an

d E

xper

imen

tal P

rob

abili

ty



Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

TI-7

3 A

ctiv

ityE

xper

imen

tal P

rob

abili

ty

Cha

pter

951

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–7

pygp

9-7

Use

you

r ca

lcul

ator

to

sim

ulat

e fl

ippi

ng a

coi

n or

rol

ling

a nu

mbe

r cu

be.T

hese

fea

ture

s ar

efo

und

in t

he M

ATH

PRB

(pro

babi

lity)

men

u.T

he c

alcu

lato

r di

spla

ys a

ran

dom

num

ber

that

repr

esen

ts h

eads

or

tails

on

a co

in o

r th

e nu

mbe

r on

a n

umbe

r cu

be.T

he c

alcu

lato

r ca

llsnu

mbe

r cu

bes

dice

. Rol

l tw

o nu

mbe

r cu

bes

100

tim

es.C

alcu

late

the

exp

erim

enta

l pro

babi

lity

ofro

lling

dou

ble-

1,do

uble

-2,d

oubl

e-3,

doub

le-4

,dou

ble-

5,or

dou

ble-

6.

Step

1C

lear

Hom

e.St

ep 2

Cho

ose

the

dice

fea

ture

in M

ATH

PRB.

[MEM

]5

7

Step

3T

he d

ispl

ay s

how

s di

ce(.

Use

2 d

ice.

Step

4In

terp

ret t

he r

esul

t and

con

tinu

e fo

r

210

0 ro

lls.

The

dis

play

sho

ws

an o

rder

ed p

air

of d

igits

, lik

e (3

5).

Thi

s m

eans

the

firs

t cub

e sh

ows

a 3

and

the

seco

nd c

ube

show

s a

5. I

f a

doub

le, l

ike

(2 2

) or

(5

5),

app

ears

, tal

ly it

in th

e ch

art b

elow

. Con

tinue

w

ith

the

next

rol

l by

pres

sing

.

Use

you

r gr

aph

ing

calc

ula

tor

to c

omp

lete

th

e fo

llow

ing.

1.C

ompl

ete

the

tabl

e fo

r 10

0 ro

lls.

Cal

cula

te th

e Fr

actio

n an

d Pe

rcen

tco

lum

ns.

See

sam

ple

dat

a.2.

The

theo

reti

cal p

roba

bili

ty o

fro

llin

g do

uble

-1 (

or a

ny o

ther

doub

le)

is 1

/36

or a

bout

3%

.C

ompa

re th

is th

eore

tica

lpr

obab

ilit

y w

ith

your

expe

rim

enta

l res

ults

.M

ost

of

the

exp

erim

enta

lp

rob

abili

ties

are

clo

se t

oth

e th

eore

tica

l.3.

Do

anot

her

expe

rim

ent,

but u

se th

e co

in f

eatu

re o

f M

ATH

PRB.

Exp

lore

the

prob

abil

ity

of a

fam

ily w

ith

thre

e ch

ildr

en h

avin

g al

l gir

ls. F

lip

3 co

ins.

Eac

h co

in s

tand

s fo

r on

e ch

ild.

If

the

resu

lt is

a 1

, the

n th

e ch

ild

is a

boy

; if

it is

0, t

hen

the

chil

d is

a g

irl.

Fli

p th

e th

ree

coin

s 10

0 ti

mes

. Tal

ly th

e re

sult

s of

3 g

irls

and

of

3 bo

ys. D

escr

ibe

your

res

ults

.

EN

TE

R

EN

TE

R

MA

TH

EN

TE

R2n

d

Dou

ble

Tal

lyN

umbe

rF

ract

ion

Per

cent

(1, 1

)||

2� 12 00�

2%

(2, 2

)|||

|4

� 14 00�4%

(3, 3

)||

2� 12 00�

2%

(4, 4

)|||

|4

� 14 00�4%

(5, 5

)|||

| ||

7� 17 00�

7%

(6, 6

)|||

3� 13 00�

3%

Tal

lyN

umbe

rF

ract

ion

Per

cent

All

gir

ls (

0, 0

, 0)

|||| |

||| |

11� 11 01 0�

11%

All

boy

s (1

, 1, 1

)|||

| ||||

10� 11 00 0�

10%

Exam

ple

1

Stu

den

ts’r

esu

lts

and

des

crip

tio

ns

will

var

y.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

950

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-7

Ro

llin

g a

Do

dec

ahed

ron

A d

odec

ahed

ron

is a

sol

id.I

t h

as t

wel

ve f

aces

,an

d ea

ch f

ace

is a

pen

tago

n.

At

the

righ

t,yo

u s

ee a

dod

ecah

edro

n w

hos

e fa

ces

are

mar

ked

wit

h

the

inte

gers

fro

m 1

th

rou

gh 1

2.Yo

u c

an r

oll

this

dod

ecah

edro

n ju

st

as y

ou r

oll

a n

um

ber

cube

.Wit

h t

he

dode

cah

edro

n,h

owev

er,t

her

e ar

e tw

elve

equ

ally

lik

ely

outc

omes

.

Ref

er t

o th

e d

odec

ahed

ron

sh

own

at

the

righ

t.F

ind

th

e p

rob

abil

ity

of e

ach

eve

nt.

1.P

(5)

� 11 2�2.

P(o

dd)

�1 2�

3.P

(pri

me)

� 15 2�4.

P(d

ivis

ible

by

5)�1 6�

5.P

(les

s th

an 4

)�1 4�

6.P

(fra

ctio

n)

0

You

can

mak

e yo

ur

own

dod

ecah

edro

n b

y cu

ttin

g ou

t th

e pa

tter

n a

t th

e ri

ght.

Fol

d al

ong

each

of

the

soli

d li

nes

.Th

en u

se t

ape

to jo

in t

he

face

s to

geth

er s

o th

at

you

r do

deca

hed

ron

loo

ks l

ike

the

one

show

n a

bove

.

7.R

oll

you

r do

deca

hed

ron

100

tim

es.R

ecor

d yo

ur

resu

lts

on a

sep

arat

e sh

eet

of p

aper

,usi

ng

a ta

ble

like

th

is.

An

swer

s w

ill v

ary.

8.U

se y

our

resu

lts

from

Exe

rcis

e 7.

Fin

d th

e ex

peri

men

tal

prob

abil

ity

for

each

of

the

even

ts

desc

ribe

d in

Exe

rcis

es 1

–6.

An

swer

s w

ill v

ary.

Outc

ome

1 2

Tally

Freq

uenc

y

1

2

3

4 5

6

7

11

12

8

9

10

2

1110

1

36

6SD

AP

3.2



An

swer

s

Exer

cise

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Co

mp

ou

nd

Eve

nts

Cha

pter

953

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–8

pygp

9-8

A c

oin

is

toss

ed a

nd

a n

um

ber

cu

be

is r

olle

d.F

ind

th

e p

rob

abil

ity

of t

ossi

ng

tail

s an

d r

olli

ng

a 5.

P(t

ails

) �

�1 2�P

(5)

��1 6�

P(t

ails

an

d 5)

��1 2�

��1 6�

or � 11 2�

So,

the

prob

abil

ity

of t

ossi

ng

tail

s an

d ro

llin

g a

5 is

� 11 2�.

MA

RB

LES

A b

ag c

onta

ins

7 b

lue,

3 gr

een

,an

d 3

red

mar

ble

s.If

Agn

es

ran

dom

ly d

raw

s tw

o m

arb

les

from

th

e b

ag,r

epla

cin

g th

e fi

rst

bef

ore

dra

win

g th

e se

con

d,w

hat

is

the

pro

bab

ilit

y of

dra

win

g a

gree

n a

nd

th

en a

blu

e m

arb

le?

P(g

reen

) �

3/13

1 13

mar

bles

, 3

are

gree

n

P(b

lue)

�7/

13

13 m

arbl

es,

7 ar

e bl

ue

P(g

reen

,th

en b

lue)

�� 13 3�

· �17 2�

�� 12 61 9�

So,

the

prob

abil

ity

that

Agn

es w

ill

draw

a g

reen

,th

en a

blu

e m

arbl

e is

� 12 61 9�.

1.F

ind

the

prob

abil

ity

of r

olli

ng

a 2

and

then

an

eve

n n

um

ber

on t

wo

con

secu

tive

rol

ls o

f a

nu

mbe

r cu

be.

� 11 2�

2.A

pen

ny

and

a di

me

are

toss

ed.W

hat

is

the

prob

abil

ity

that

th

e pe

nn

yla

nds

on

hea

ds a

nd

the

dim

e la

nds

on

tai

ls?

�1 4�

3.L

azlo

’s s

ock

draw

er c

onta

ins

8 bl

ue

and

5 bl

ack

sock

s.If

he

ran

dom

lypu

lls

out

one

sock

,wh

at i

s th

e pr

obab

ilit

y th

at h

e pi

cks

a bl

ue

sock

?

� 18 3�

A c

om

po

un

d e

ven

tco

nsis

ts o

f tw

o or

mor

e si

mpl

e ev

ents

.If

the

outc

ome

of o

ne e

vent

doe

s no

t af

fect

the

outc

ome

of a

sec

ond

even

t, th

e ev

ents

are

cal

led

ind

epen

den

t ev

ents

.The

pro

babi

lity

of t

wo

inde

pend

ent

even

ts c

an b

e fo

und

by m

ultip

lyin

g th

e pr

obab

ility

of

the

first

eve

nt b

y th

e pr

obab

ility

of

the

seco

nd e

vent

.

Exam

ple

1

Exam

ple

2

6SD

AP

3.4,

6S

DA

P3.

5

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Less

on R

eadi

ng G

uide

Co

mp

ou

nd

Eve

nts

Cha

pter

952

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-8

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n a

t th

e to

p o

f p

age

492

in y

our

text

boo

k.W

rite

you

r an

swer

s b

elow

.

1.W

hat

is

the

prob

abil

ity

of O

mar

bei

ng

in t

he

seco

nd

hea

t? i

n L

ane

3?�1 4�;

�1 5�

2.M

ult

iply

you

r an

swer

s in

Exe

rcis

es 1

.Wh

at d

oes

this

nu

mbe

r re

pres

ent?

� 21 0�;

the

pro

bab

ility

of

Om

ar b

ein

g in

lan

e 3

of

the

seco

nd

hea

t

Rea

d t

he

Less

on

Use

th

e in

trod

uct

ion

to

the

less

on t

o an

swer

Exe

rcis

es 4

–6.

3.W

hat

doe

s a

com

pou

nd

even

t co

nsi

st o

f?It

co

nsi

sts

of

two

or

mo

resi

mp

le e

ven

ts.

4.D

efin

e in

depe

nde

nt

even

ts.

Th

ey a

re t

wo

eve

nts

in w

hic

h t

he

ou

tco

me

of

on

e,d

oes

no

t af

fect

th

e o

utc

om

e o

f th

e o

ther

.

5.W

rite

th

e pr

obab

ilit

y of

in

depe

nde

nt

even

ts i

n s

ymbo

ls.

P(A

an

d B

) �

P(A

) �

P(B

)

6.H

ow c

an y

ou f

ind

the

prob

abil

ity

of t

wo

inde

pen

den

t ev

ents

?S

amp

lean

swer

:M

ult

iply

th

e p

rob

abili

ty o

f th

e fi

rst

even

t by

th

ep

rob

abili

ty o

f th

e se

con

d e

ven

t.

Rem

emb

er W

hat

Yo

u L

earn

ed7.

Lis

t se

vera

l in

depe

nde

nt

com

pou

nd

even

ts.E

xpla

in w

hy

you

con

side

r th

eev

ents

to

be i

nde

pen

den

t.S

amp

le a

nsw

er:

spin

nn

ing

a s

pin

ner

and

flip

pin

g a

co

in.T

hey

hav

e n

o e

ffec

t o

n e

ach

oth

er.6S

DA

P3.

4, 6

SD

AP

3.5



A n

um

ber

cu

be

is r

olle

d a

nd

a s

pin

ner

lik

e th

e on

e sh

own

is

spu

n.

Fin

d e

ach

pro

bab

ilit

y.

1.P

(6 a

nd

D)

� 21 4�2.

P(m

ult

iple

of

2 an

d B

)�1 8�

3.P

(not

6 a

nd

not

A)

�5 8�

A s

et o

f 7

card

s is

lab

eled

1–7

.A s

econ

d s

et o

f 12

car

ds

con

tain

s th

e fo

llow

ing

colo

rs:3

gre

en,6

red

,2 b

lue,

and

1 w

hit

e.O

ne

card

fro

m e

ach

set

is

sele

cted

.Fin

dea

ch p

rob

abil

ity.

4.P

(6 a

nd

gree

n)

� 21 8�5.

P(p

rim

e an

d bl

ue)

� 22 1�6.

P(o

dd a

nd

red)

�2 7�

7.P

(7 a

nd

wh

ite)

� 81 4�8.

P(m

ulti

ple

of 3

and

red

)�1 7�

9.P

(eve

n a

nd

wh

ite)

� 21 8�

A c

oin

is

toss

ed,a

nu

mb

er c

ub

e is

rol

led

,an

d a

let

ter

is p

ick

ed f

rom

the

wor

d f

ram

er.

10.

P(t

ails

,5,m

)� 71 2�

11.

P(h

eads

,odd

,r)

� 11 2�12

.P

(hea

ds,6

,vow

el)

� 31 6�

13.

P(t

ails

,pri

me,

cons

onan

t)14

.P

(not

tai

ls,m

ulti

ple

of 3

,a)

15.

P(n

ot h

eads

,2,f

)� 71 2�

�1 6�� 31 6�

16.

TOLL

RO

AD

Mr.

Esp

inoz

a ra

ndo

mly

ch

oose

s on

e of

fiv

e to

ll b

ooth

s w

hen

ente

rin

g a

toll

roa

d w

hen

dri

vin

g to

wor

k.W

hat

is

the

prob

abil

ity

he

wil

lse

lect

th

e m

iddl

e to

ll b

ooth

on

Mon

day

and

Tu

esda

y?� 21 5�

MA

RB

LES

For

Exe

rcis

es 1

7–20

,use

th

ein

form

atio

n i

n t

he

tab

le s

how

n t

o fi

nd

eac

hp

rob

abil

ity.

Aft

er a

mar

ble

is

ran

dom

ly p

ick

edfr

om a

bag

con

tain

ing

mar

ble

s of

fou

r d

iffe

ren

tco

lors

,th

e co

lor

of t

he

mar

ble

is

obse

rved

an

dth

en i

t is

ret

urn

ed t

o th

e b

ag.

17.

P(r

ed)

� 11 2�18

.P

(gre

en,b

lue)

� 21 4�

19.

P(r

ed,w

hit

e,bl

ue)

� 91 6�20

.P

(blu

e,bl

ue,

blu

e)� 61 4�

A D

CB

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice

Co

mp

ou

nd

Eve

nts

Cha

pter

955

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–8

pygp

9-8

Mar

ble

sC

olor

Nu

mb

erW

hit

e6

Gre

en2

Red

1B

lue

3

6SD

AP

3.4,

6S

DA

P3.

5

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Skill

s Pr

actic

eC

om

po

un

d E

ven

ts

Cha

pter

954

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-8

1.F

our

coin

s ar

e to

ssed

.Wh

at i

s th

e pr

obab

ilit

y of

tos

sin

g al

l h

eads

?

� 11 6�

2.O

ne

lett

er i

s ra

ndo

mly

sel

ecte

d fr

om t

he

wor

d P

RIM

E a

nd

one

lett

er i

sra

ndo

mly

sel

ecte

d fr

om t

he

wor

d M

AT

H.W

hat

is

the

prob

abil

ity

that

both

let

ters

sel

ecte

d ar

e vo

wel

s?

� 11 0�

3.A

car

d is

ch

osen

at

ran

dom

fro

m a

dec

k of

52

card

s.It

is

then

rep

lace

dan

d a

seco

nd

card

is

chos

en.W

hat

is

the

prob

abil

ity

of g

etti

ng

a ja

ck a

nd

then

an

eig

ht?

� 11 69�

For

Exe

rcis

es 4

–6,u

se t

he

info

rmat

ion

bel

ow.

A s

tan

dard

dec

k of

pla

yin

g ca

rds

con

tain

s 52

car

ds i

n f

our

suit

s of

13

card

sea

ch.T

wo

suit

s ar

e re

d an

d tw

o su

its

are

blac

k.F

ind

each

pro

babi

lity

.Ass

um

eth

e fi

rst

card

is

repl

aced

bef

ore

the

seco

nd

card

is

draw

n.

4.P

(bla

ck,q

uee

n)

5.P

(bla

ck,d

iam

ond)

6.P

(jac

k,qu

een

)

� 21 6��1 8�

� 11 69�

7.W

hat

is

the

prob

abil

ity

of s

pin

nin

g a

nu

mbe

r gr

eate

r th

an 5

on

a s

pin

ner

nu

mbe

red

1 to

8 a

nd

toss

ing

a ta

il o

n a

coi

n?

� 13 6�

8.T

wo

card

s ar

e ch

osen

at

ran

dom

fro

m a

sta

nda

rd d

eck

of c

ards

wit

hre

plac

emen

t.W

hat

is

the

prob

abil

ity

of g

etti

ng

2 ac

es?

� 11 69�

9.A

CD

rac

k h

as 8

cla

ssic

al C

Ds,

5 po

p C

Ds,

and

3 ro

ck C

Ds.

On

e C

D i

sch

osen

an

d re

plac

ed,t

hen

a s

econ

d C

D i

s ch

osen

.Wh

at i

s th

e pr

obab

ilit

yof

ch

oosi

ng

a ro

ck C

D t

hen

a c

lass

ical

CD

?

� 33 2�

10.

A ja

r h

olds

15

red

pen

cils

an

d 10

blu

e pe

nci

ls.W

hat

is

the

prob

abil

ity

ofdr

awin

g on

e re

d pe

nci

l fr

om t

he

jar?

�3 5�

6SD

AP

3.4,

6S

DA

P3.

5



An

swer

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enri

chm

ent

Cha

pter

957

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Lesson 9–8

pygp

9-8

Co

mp

ou

nd

Eve

nts

Th

e ga

me

of r

oule

tte

is p

laye

d by

dro

ppin

g a

ball

into

a s

pin

nin

g,bo

wl-

shap

ed w

hee

l.W

hen

th

ew

hee

l st

ops

spin

nin

g,th

e ba

ll w

ill

com

e to

res

t in

any

of 3

8 lo

cati

ons.

On

a r

oule

tte

wh

eel,

the

eigh

teen

eve

n n

um

bers

from

2 t

hro

ugh

36

are

colo

red

red

and

the

eigh

teen

odd

nu

mbe

rs f

rom

1 t

hro

ugh

35

are

colo

red

blac

k.T

he

nu

mbe

rs 0

an

d 00

are

col

ored

gree

n.

To

fin

d th

e pr

obab

ilit

y of

tw

o in

depe

nde

nt

even

ts,

the

resu

lts

of t

wo

spin

s,fi

nd

the

prob

abil

ity

ofea

ch e

ven

t fi

rst.

P(r

ed)

��1 38 8�

or � 19 9�

P(b

lack

) �

�1 38 8�or

� 19 9�

Th

en m

ult

iply

.

P(r

ed,t

hen

bla

ck)

�� 19 9�

�� 19 9�

or � 38 61 1�

Fin

d e

ach

pro

bab

ilit

y.

1.bl

ack,

then

bla

ck

� 38 61 1�

2.pr

ime

nu

mbe

r,th

en a

com

posi

te n

um

ber

�1 73 25 2�

3.a

nu

mbe

r co

nta

inin

g at

lea

st o

ne

0,th

en a

nu

mbe

r co

nta

inin

g at

lea

ston

e 2

� 1,6 45 44�

4.re

d,th

en b

lack

� 38 61 1�

5.th

e n

um

bers

rep

rese

nti

ng

you

r ag

e,m

onth

of

birt

h,a

nd

then

day

of

birt

h

� 54,1 87

2�

03

915

20

32 26 4 10 16 21 33 27 5

1117

2234

2800

612

2335291871312430368

214

1931

25

6SD

AP

3.4,

6S

DA

P3.

5

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Wor

d Pr

oble

m P

ract

ice

Co

mp

ou

nd

Eve

nts

Cha

pter

956

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6

Copyright © Glencoe\McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

9-8

1.SA

FETY

Eig

hty

per

cen

t of

all

Cal

ifor

nia

driv

ers

wea

r se

at b

elts

.If

thre

e dr

iver

sar

e pu

lled

ove

r,w

hat

is

the

prob

abil

ity

that

all

wou

ld b

e w

eari

ng

thei

r se

atbe

lts?

Wri

te a

s a

perc

ent

to t

he

nea

rest

ten

th.

51.2

%

2.V

EGET

AB

LES

A n

atio

nw

ide

surv

eysh

owed

th

at 6

5% o

f al

l ch

ildr

en i

n t

he

Un

ited

Sta

tes

disl

ike

eati

ng

vege

tabl

es.

If t

hre

e ch

ildr

en a

re c

hos

en a

t ra

ndo

m,

wh

at i

s th

e pr

obab

ilit

y th

at a

ll t

hre

edi

slik

e ea

tin

g ve

geta

bles

? W

rite

as

ape

rcen

t to

th

e n

eare

st t

enth

.27

.5%

3.Q

UA

LITY

In a

sh

ipm

ent

of 5

0ca

lcu

lato

rs,4

are

def

ecti

ve.O

ne

calc

ula

tor

is r

ando

mly

sel

ecte

d an

dte

sted

.Wh

at i

s th

e pr

obab

ilit

y th

at i

t is

defe

ctiv

e?

� 22 5�

4.M

AR

BLE

SA

bag

con

tain

s 6

gree

nm

arbl

es,2

blu

e m

arbl

es,a

nd

3 w

hit

em

arbl

es.G

wen

dra

ws

one

mar

ble

from

the

jar

and

repl

aces

it.

Jeff

th

en d

raw

son

e m

arbl

e fr

om t

he

jar.

Wh

at i

s th

epr

obab

ilit

y th

at G

wen

dra

ws

a bl

ue

mar

ble

and

Jeff

dra

ws

a w

hit

e m

arbl

e?� 16 21�

5.D

EMO

NST

RA

TIO

NM

s.M

orri

s n

eeds

ast

ude

nt

to h

elp

her

wit

h a

dem

onst

rati

on f

or h

er c

lass

of

12 g

irls

and

14 b

oys.

Sh

e ra

ndo

mly

ch

oose

s a

stu

den

t.W

hat

is

the

prob

abil

ity

that

she

choo

ses

a gi

rl?

� 16 3�

6.SU

RV

EYR

ube

n s

urv

eyed

his

cla

ss a

nd

fou

nd

that

4 o

ut

of 2

2 st

ude

nts

wal

k to

sch

ool.

If o

ne

of t

he

22 s

tude

nts

is

sele

cted

at

ran

dom

,wh

at i

s th

epr

obab

ilit

y th

at t

he

chos

en s

tude

nt

DO

ES

NO

T w

alk

to s

choo

l?

� 19 1�

6SD

AP

3.4,

6S

DA

P3.

5



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

TI-7

3 A

ctiv

ityP

rob

abili

ty a

nd

Per

cen

ts

Cha

pter

958

Gle

ncoe

Cal

iforn

ia M

athe

mat

ics,

Gra

de 6


9-8

Whe

n yo

u so

lve

prob

abili

ty p

robl

ems,

use

your

cal

cula

tor

to e

xpre

ss f

ract

ions

as

deci

mal

san

d pe

rcen

ts.

Tw

o nu

mbe

r cu

bes

are

rolle

d.F

ind

the

prob

abili

ty t

hat

both

cub

es s

how

an

odd

num

ber.

Rep

ort

the

prob

abili

ty a

s a

perc

ent.

The

pro

babi

lity

of

a cu

be s

how

ing

an o

dd n

umbe

r is

�1 2� . T

o fi

nd th

e pr

obab

ilit

yth

at b

oth

firs

t and

sec

ond

cube

s ar

e od

d, m

ulti

ply

�1 2�by

�1 2� .

Key

s: 1

2

1 2

Dis

play

: � 21 �

* � 21 �

� 41 �

� 41 �.25

100

Ans

*100

25

The

pro

babi

lity

that

bot

h cu

bes

show

odd

num

bers

is 2

5%.

The

re a

re 3

red

mar

bles

and

5 b

lue

mar

bles

in a

bag

.Tw

o m

arbl

es a

re d

raw

nan

d th

e fi

rst m

arbl

e is

rep

lace

d be

fore

the

seco

nd is

dra

wn.

Wha

t is

the

prob

abili

ty o

f dra

win

g 2

blue

mar

bles

? R

epor

t the

pro

babi

lity

as a

per

cent

.

Key

s:

Dis

play

:

5 8

5 8

� 85 � *� 85 �

� 625 4�

Dis

play

:�625 4�

0.390

625

100

Dis

play

:Ans

*100

0.390

625

The

pro

babi

lity

of

draw

ing

2 bl

ue m

arbl

es is

39.

06%

.

Fin

d e

ach

pro

bab

ilit

y.R

epor

t yo

ur

answ

er a

s a

per

cen

t.R

oun

d p

erce

nts

to

the

nea

rest

hu

nd

red

th w

hen

nec

essa

ry.

1.Y

ou d

raw

2 m

arbl

es f

rom

a b

ag r

epla

cing

the

firs

t mar

ble

befo

re d

raw

ing

the

seco

nd. T

he b

agco

ntai

ns 4

yel

low

mar

bles

, 2 w

hite

mar

bles

, and

6 r

ed m

arbl

es.

a.W

hat i

s th

e pr

obab

ilit

y th

at y

our

firs

t mar

ble

is r

ed a

nd th

e se

cond

is y

ello

w?

16.6

7%b.

Wha

t is

the

prob

abil

ity

that

bot

h m

arbl

es a

re w

hite

?2.

78%

c.W

hat i

s th

e pr

obab

ilit

y th

at n

eith

er m

arbl

e is

red

?25

%d.

Wha

t is

the

prob

abil

ity

that

bot

h m

arbl

es a

re r

ed?

25%

2.Y

ou h

ave

thre

e nu

mbe

r cu

bes.

a.W

hat i

s th

e pr

obab

ilit

y th

at y

ou w

ill r

oll a

ll e

ven

num

bers

?12

.5%

b.W

hat i

s th

e pr

obab

ilit

y th

at y

ou w

ill r

oll o

nly

num

bers

less

than

3?

3.70

%c.

CH

ALL

ENG

EW

hat i

s th

e pr

obab

ilit

y th

at y

ou w

ill r

oll a

1 o

n on

ly o

ne n

umbe

r cu

be?

27.7

8%

EN

TE

R

EN

TE

RF

D

EN

TE

Rb

cb

c

EN

TE

R

EN

TE

RF

D

EN

TE

Rb

cb

c

F D←

←

F D←

←

Exam

ple

1

Exam

ple

2




An

swer

s

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.Chapter 9 Assessment Answer Key

Quiz 1 (Lessons 9-1 and 9-2) Quiz 3 (Lessons 9-5 and 9-6) Mid-Chapter TestPage 61 Page 62 Page 63

Quiz 2 (Lessons 9-3 and 9-4)

Page 61Quiz 4 (Lessons 9-7 and 9-8)

Page 62

1.

2.

3.

4.

5. C

See students’ work.There are 24

arrangements.

�1136�

�12

�

�12

�

1.

2.

3.

4.

5. 40,320

120

756

824

1.

2.

3.

4.

5. 30

6

84

210

126

1.

2.

3.

4.

5.�210�

�152�

�16�; Sample answer:

The theoreticalprobability is less

than the experimentalprobability.

�25

�

�13

�

7.

8.

9.

10.

11.

12.

13. 140

9

8

120

30

64

1.

2.

3.

4.

5.

6. J

B

F

B

G

B

Chapter 9 Assessment Answer KeyVocabulary Test Form 1Page 64 Page 65 Page 66

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Sample answer: If eventM can occur in m waysand is followed by eventN that can occur in nways, then event Mfollowed by N can occurin m � n ways.

compound event

fair game

combination

probability

permutation

complementary event

sample space

independent event

experimentalprobability

outcome 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. H

C

G

D

J

C

H

A

G

A

G

D 13.

14.

15.

16.

17.

18.

19.

20. F

D

F

B

F

C

J

C

B:�315�


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.


An

swer

s

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In


Form 2A Form 2BPage 67 Page 68 Page 69 Page 70

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. H

D

G

A

F

B

J

B

H

A

G

D 13.

14.

15.

16.

17.

18.

19.

20. G

C

H

C

H

B

J

A

B:�210�

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. A

J

B

F

C

J

B

H

C

H

D

B:�115�

12.

13.

14.

15.

16.

17.

18.

19.

20. G

B

G

B

F

B

J

B

J


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.Chapter 9 Assessment Answer Key

Form 2CPage 71 Page 72

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. permutation; 720

combination; 126

combination; 15

permutation; 210

144

240

1,512

�14

�

�12

�

See students’ work.There are 12 possible

ornaments.

See students’ work.There are

24 possibilities.12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 3,276,000

�1415�

�2156�

�314�

It is less than theexperimentalprobability.

�59

�

�47

�

�37

�

91

136,080


An

swer

s

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In


Form 2DPage 73 Page 74

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. combination; 35

permutation; 120

permutation; 56

combination; 120

18

12

450

�14

�

�12

�


possible orders.


arrangements. 12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 468,000

�121�

�112�

�114�


�13

�

�25

�

�35

�

165

544,320


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.Chapter 9 Assessment Answer Key

Form 3Page 75 Page 76

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

permutation;15,600

combination; 35

combination; 70

permutation; 720

24

480

441

�58

�

�12

�


song types.


arrangements.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 7,862,400

�5,5

125�

�1114�

�245�


�38

�

�35

�

�35

�

220

3,276,000

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.


An

swer

s

Chapter 9 Assessment Answer Key Page 77, Extended-Response Test

Scoring Rubric

Level Specific Criteria

4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.

3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.

2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.

1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.

0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.


Chapter 9 Assessment Answer Key Page 77, Extended-Response Test

Sample Answers

1. a. There are 4 possible outcomeshaving an equal chance of occurring.

number of ways to spin a 1

number of possible outcomes

b. Spin spinner B 100 times and tallythe number of times you spin W.

P(W) � �1n00�

number of times you spin W

2. a.

b. If the outcome of one event does notinfluence the outcome of a secondevent, the events are calledindependent events.

c. To find the probability of tossing ahead and drawing a red marble,write the number of ways to toss ahead and draw a red marble (2) overthe number of possible outcomes.P(H, R) � P(H) · P(R) � �

12� · �

26� � �

16�,

since they are independent events.

d. P(B, then B) � P(B) · P(B after B)

� �12� · �

25� � �

15�

The probability of the first event is �12�

because �12� of the marbles are blue.

The probability of the second event

is �25� because the blue marble drawn

was not replaced. Two of theremaining five marbles are blue.

3. a. Each time Rayna chooses one of eachtype of relative is an event. Theevent of choosing a niece can occurin 8 ways, choosing a nephew canoccur in 9 ways, and so on. So, Raynacould choose a possible 8 � 9 � 6 � 3 � 5 � 6,480 teams.

b. 8 � 7 � 6 � 5 � 4 � 3 � 2 � 1 � 40,320;The order of the arrangement of the nieces is important, so apermutation, is used.

c.

� 44,352,165

The order of their arrangement isnot important, so a combination isused.

31 � 30 � 29 � 28 �27 � 26 � 25 � 24 � 23 � 22��10 � 9 � 8 � 7 � 6 � 5 �

4 � 3 � 2 � 1

H

MarbleDraw

CoinToss

SampleSpace

W HWHB1HB2HB3HR1HR2

B3

B2

B1

R1R2

T

W TWTB1TB2TB3TR1TR2

B3

B2

B1

R1R2

→

→

→

P(1) � �14�

In addition to the scoring rubric found on page A33, the following sample answersmay be used as guidance in evaluating extended-response assessment items.

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.


An

swer

s

Chapter 9 Assessment Answer KeyStandardized Test PracticePage 78 Page 79

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D 13.

14.

15.

16.

17.

18.

19. A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.


Chapter 9 Assessment Answer KeyStandardized Test PracticePage 80

20.

21.

22.

23.

24.

25a.

25b.

There are 8 people,so the number ofarrangements is 8! � 40,320.

Order is important,so this is apermutation. Thereare 3 women, 3 men,and 2 children so the number of waysto arrange them is(3!)(3!)(2!) � 72.

1,716

13%

1�38

�

�245�

20


An

swer

s

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In


Unit 4 Test

Page 81 Page 82

1.

2.

3.

4.

5.

6.

7.

8.

Sample answer: Thevertical axis does not startat zero. Therefore, itexaggerates the number oftelevisions for the USA. Itlooks double that of Japan.

15

$8; $7; $5

Sample answer:110 mm

Sample answer:Cluster 69–76; gaps

65–69, 76–78; nooutliers

72 mph

169.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.independent; �2

100�

permutation;39, 916, 800

combination;3,003

1,360

See students’ treediagrams; 18outcomes

�23

�

�16

�

�12

�

�13

�

�16

�

�1531�

�14

�

Stem Leaf2 5 93 5 84 0 3 5 7 5 0 6

3|2 � 32

chapter 9 resource masters - mhschooliv teacher’s guide to using the chapter 9 resource masters...

Documents