chapter 12 practice test #1 - m2...

Chapter 12 Practice Test #1

Class Name : M29 Geometry - 2019-20 Term 2 Instructor Name : Mr. Beckey

Student Name : _____________________ Instructor Note :

1. The lunch special at Frank's Restaurant is a sandwich, a drink and a dessert. There are sandwiches, drink, and desserts to choose from. How many lunch specials are possible?

2. Monroe High School is going to select a committee. The committee will have a faculty member, a male student, a femalestudent, and a parent.

Here are the positions and the people interested in each.

Position People interested

Faculty member Mr. Kim, Ms. Kelly

Male student Shen, Dan, Chau, Keith

Female student Mai, Raina, Maya, Jina

Parent Mr. Rodriguez, Dr. Miller, Mrs. Robinson, Dr. Collins, Mrs. Richardson

Based on this list, how many ways are there to fill the four committee positions?

3. A bag has six balls labeled , , , , , and .One ball will be randomly picked, and its letter will be recorded as the outcome.

Give the sample space describing all possible outcomes.

Then give all of the outcomes for the event of choosing a letter from to .If there is more than one element in the set, separate them with commas.

Sample space:

Event of choosing a letter from to :

4. A class is choosing a president, a vice president, and a treasurer.

2 1 6

A B C D E F

D F

D F

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4. A class is choosing a president, a vice president, and a treasurer.

There are two students running for president: Maria and Linda.There are two students running for vice president: Bob and John.There are three students running for treasurer: Jessica, Amanda, and Debra.

The tree diagram below shows the possible outcomes. Use the diagram to answer the questions.

(a) How many outcomes are there?

(b) How many outcomes have both Maria and John being chosen?

(c) How many outcomes have Jessica or Amanda being chosen?

5. A burger chain wants to send codes for a free small drink to the members of its kids club. The coupon code will have one

letter, followed by two digits, followed by two letters. The letters , , , and and the digit will not be used. So, there are

letters and digits that will be used. Assume that the letters and digits can be repeated. How many such coupon codescan be generated?

6. A bag with marbles is shown below. ( marbles are grey, is black, and are white.) A marble is chosen from the bag

R S T U 322 9

6 2 1 3

President

Maria

Linda

Vice President

Bob

John

Bob

John

Treasurer

Jessica

Amanda

Debra

Jessica

Amanda

Debra

Jessica

Amanda

Debra

Jessica

Amanda

Debra

Outcome

, Maria , Bob Jessica

, Maria , Bob Amanda

, Maria , Bob Debra

, Maria , John Jessica

, Maria , John Amanda

, Maria , John Debra

, Linda , Bob Jessica

, Linda , Bob Amanda

, Linda , Bob Debra

, Linda , John Jessica

, Linda , John Amanda

, Linda , John Debra


6. A bag with marbles is shown below. ( marbles are grey, is black, and are white.) A marble is chosen from the bagat random. What is the probability that it is grey?

Write your answer as a fraction in simplest form.

7. Here is a table showing all cards in a standard deck.

Face cards

Color Suit Ace Two Three Four Five Six Seven Eight Nine Ten Jack Queen King

Red Hearts ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥ ♥Red Diamonds ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

Black Spades ♠ ♠ ♠ ♠ ♠ ♠ ♠ ♠ ♠ ♠ ♠ ♠ ♠Black Clubs ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣

Suppose one card is drawn at random from a standard deck.Answer each part. Write your answers as fractions in simplest form.

8. An organization will give a prize to a local artist. The artist will be randomly chosen from among painters, sculptors, and

6 2 1 3

52

AA 22 33 44 55 66 77 88 99 1010 JJ QQ KK

AA 22 33 44 55 66 77 88 99 1010 JJ QQ KK

AA 22 33 44 55 66 77 88 99 1010 JJ QQ KK

AA 22 33 44 55 66 77 88 99 1010 JJ QQ KK

(a) What is the probability that the card drawn is a black card?

(b) What is the probability that the card drawn is a four?

(c) What is the probability that the card drawn is a black card or a four?

3 7© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 12 Pr ac t i ce T es t #1 / 20

8. An organization will give a prize to a local artist. The artist will be randomly chosen from among painters, sculptors, and

photographers. What is the probability that the artist chosen will be a painter or a sculptor?


9.

(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter theprobability of the event.

(b) Subtract.

(c) Select the answer that makes the sentence true.

is the same as________

•

• not

• not • None of the above

10. There are people taking part in a raffle.

Ann, Bob, Elsa, Jim, Kira, Lena, Omar, and Soo.

Suppose that prize winners are randomly selected from the people.

Compute the probability of each of the following events.

Event A: The first four prize winners are Soo, Ann, Lena, and Jim, regardless of order.

Event B: Kira is the first prize winner, Soo is second, Bob is third, and Elsa is fourth.

Write your answers as fractions in simplest form.

11. Evaluate.

3 712

EventOutcomes

Probability1 2 3 4 5 6 7 8 9 10

X ________=P X

not X not ________−1 P =X

=−1 P X

−1 P X

P X

P X−1 P X

8

8

=P A

=P B


11. Evaluate.

Simplify your answer as much as possible.

12. Evaluate and .

13. Suppose we want to choose colors, without replacement, from the colors red, blue, green, and purple.

(a) How many ways can this be done, if the order of the choices is taken into consideration?

(b) How many ways can this be done, if the order of the choices is not taken into consideration?

14. Suppose we want to choose colors, without replacement, from distinct colors.

(a) How many ways can this be done, if the order of the choices is relevant?

(b) How many ways can this be done, if the order of the choices is not relevant?

15. Answer the questions below.

16. There are runners in a race. There will be a first-place, a second-place, and a third-place prize awarded. In how many

different ways can the prizes be awarded?

17. A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded

!4 !8!2 !7

12P 3 8C 4

2 4

6 9

53


17. A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded

circular region. The radius of the dartboard is , and the radius of the shaded region is .

Use the value for . Round your answer to the nearest hundredth.

18. For each experiment, determine whether events A and B are independent or dependent.

Experiment Events Independent Dependent

A deck contains cards numbered through . A card is randomlyselected and reinserted into the deck. The deck is shuffled. Then anotherrandom selection is made.

Event A: The first

selection is a .

Event B: Thesecond selection is

a .

Rafael randomly selects a sock from a drawer containing black socks andbrown socks, and puts it on. Then another random selection is made fromthe remaining socks.

Event A: The firstselection is black.

Event B: Thesecond selection isbrown.

A family has two children.

Event A: The olderchild has red hair.

Event B: Bothchildren have redhair.

A number cube with sides labeled through is rolled twice.

Event A: The first

roll is a .

Event B: The

second roll is a .

A litter of puppies consists of black puppies and white puppies. A puppy israndomly selected and removed from the litter. Then another randomselection is made from the remaining puppies.

Event A: The firstselection is a whitepuppy.

Event B: Thesecond selection isa black puppy.

19. A spinner has equally sized sections, of which are gray and of which are blue. The spinner is spun twice. What is

9 in 3 in

3.14 π

13 1 13 6

7

1 62

1

10 6 4

9 in

3 in


19. A spinner has equally sized sections, of which are gray and of which are blue. The spinner is spun twice. What isthe probability that the first spin lands on gray and the second spin lands on blue ?


20. A bag contains marbles: are green, are red, and are blue. Isabel chooses a marble at random, and withoutputting it back, chooses another one at random. What is the probability that the first marble is green and the second is red?Write your answer as a fraction in simplest form.

21. A city planner surveyed residents. For each, the planner recorded whether the resident owns a car and whether theresident lives alone. The results are summarized in the table below.

Alone Not alone

Car

No car

Suppose a resident from the survey is chosen at random. Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.

22. A marble is selected from a bag containing eight marbles numbered to .

The number on the marble selected will be recorded as the outcome.

Consider the following events.

Event : The marble selected has a number less than .

Event : The marble selected has an odd number.

Give the outcomes for each of the following events.If there is more than one element in the set, separate them with commas.

Event " or ":

Event " and ":

The complement of the event :

23. The Venn diagram below shows the students in Mr. Hernandez's class.

10 6 4

9 2 5 2

171

9 51

40 71

(a) What is the probability that the resident does not live alone?

______

(b) What is the probability that the resident does not own a car or does not live alone?

______

1 8

A 4B

A B

A B

A

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23. The Venn diagram below shows the students in Mr. Hernandez's class.The diagram shows the memberships for the Computer Club and the Tennis Club.

Note that "Keisha" is outside the circles since she is not a member of either club.

One student from the class is randomly selected.

Let denote the event "the student is in the Computer Club."

Let denote the event "the student is in the Tennis Club."

(a) Find the probabilities of the events below.Write each answer as a single fraction.

(b) Select the probability that is equal to .

24. A spinner has equally sized slices numbered from to

16

A

B

=P A

=P B

=P A andB

=P A orB

=+P A −P B P A and B

+P A −P B P A and B

P A and BP A

P B

P A or B

6 1 6

Computer Tennis

Austin

Jenny

Kira

Latoya

Jim

Deon

Frank

Mai

Donna

Chang

Michael

Keisha

Elsa

Kaitlin

Ryan

Omar


24. A spinner has equally sized slices numbered from to . Some are white and some are grey, as shown below.

Answer the following questions. Write each answer as a fraction.

The wheel will be spun and will stop on a slice at random.

(a) What is the probability that the wheel stops on a slice with a number less than ?

(b) What is the probability that the wheel stops on a slice with a number less than , given that the wheel stops on a greyslice?

25. Suppose that of all adults suffer from diabetes and that of all adults are obese. Suppose also that of alladults both are obese and suffer from diabetes.

(a) Find the probability that a randomly chosen adult who is obese also suffers from diabetes. Round youranswer to the nearest hundredth.

(b) Find the probability that a randomly chosen adult is obese, given that he or she suffers from diabetes. Roundyour answer to the nearest hundredth.

26. For each set of probabilities, determine whether the events and are independent or dependent.

27. The Venn diagram shows the memberships for the Music, Computer, and Spanish clubs.

6 1 6

5 5

3% 29 % 1%

A B

Probabilities Independent Dependent

; ; and =P A12 = P B

14 P A =B

18

; ;=P A13 = P B

16 = P B |A

12

; ;=P A12 = P B

16 = P A |B

12

; ;=P A16 = P B

14 = P A |B

15


27. The Venn diagram shows the memberships for the Music, Computer, and Spanish clubs.Use the diagram to answer the questions below.

(a) Select all the clubs that Salma is a member of.(b) How many students are members of the Spanish Club or the Computer Club (or both)?(c) Which of these students are in only one club?

28. Each of sixty-five students in grade 7 or 8 was asked, "What is your favorite sport?"

Here are the results.

students in seventh grade and students in eighth grade chose "Hockey".

students in seventh grade and students in eighth grade chose "Football".

students in seventh grade and students in eighth grade chose "Basketball".

Construct a two-way frequency table for the data.

Hockey Football Basketball

Seventhgrade

Eighthgrade

29. Each of thirty-five students in grade 7 or 8 was asked, "What is your favorite sport?"

13 67 1215 12

Music Computer

Spanish

SalmaFrank

Chau

Lucy

Keith

Dale

YokoBill

Joe

Susan


29. Each of thirty-five students in grade 7 or 8 was asked, "What is your favorite sport?"

Here are the results.

students in seventh grade and students in eighth grade chose "Swimming".

students in seventh grade and students in eighth grade chose "Baseball".

Construct a two-way frequency table for the data.

30. At a school's open house, T-shirts and sweatshirts were sold.Each item was purchased by either a student or a parent.

The two-way frequency table summarizes a random sample of items sold that night.

Student Parent

T-shirt

Sweatshirt

Let T-shirt be the event that an item randomly chosen from among those sold was a T-shirt.

Let parent be the event that an item randomly chosen from among those sold was purchased by a parent.

Find the following probabilities. Write your answers as decimals.

(a) P(parent) _____

(b) P(T-shirt and parent) _____

(c) P(T-shirt | parent) _____

31. A group of patients tested a new medication.

11 68 10

70

18 2117 14

=

=

=


31. A group of patients tested a new medication.Some tried the new medication, and the rest took the old medication.

The results are reported in the following two-way frequency table.

No improvement Improvement

Old medication

New medication

A patient is chosen at random from this group.

Complete the following. Write your answers as decimals.

(a) Find the probability that the patient showed improvement.

P(improvement) _____

(b) Find the probability that the patient showed improvement, given that he took the newmedication.

P(improvement | new medication) _____

(c) Is there evidence that a patient who takes the new medication is more likely to showimprovement than a randomly chosen patient from the group?

Yes, because the probability found in part (b) is much greater than theprobability found in part (a).

No, because the probability found in part (b) is much greater than the probabilityfound in part (a).

Yes, because the probability found in part (a) is much greater than theprobability found in part (b).

No, because the probability found in part (a) is much greater than the probabilityfound in part (b).

Yes, because the probability found in part (b) is about the same as theprobability found in part (a).

No, because the probability found in part (b) is about the same as the probabilityfound in part (a).

32. A movie club surveyed high school students. The students were asked how often they go to the movies and whether

125

28 3727 33

=

=


32. A movie club surveyed high school students. The students were asked how often they go to the movies and whetherthey prefer action movies or comedies. Their responses are summarized in the following table.

Twice a month

or lessThree times a month

or more

Action

Comedy

(a) What percentage of the students go to the movies twice a month or less?

(b) What percentage of the students prefer comedies ?

33.

Highest degree earned

No college degree Two-year degree Four-year degree Advanced degree

Place of residence

Urban 20 40 19 19

Suburban 24 50 31 40

Rural 15 31 37 48

What is the relative frequency of people in the sample whose place of residence is suburban?

Round your answer to two decimal places.

150

48 2463 15


Chapter 12 Practice Test #1 Answers for class M29 Geometry - 2019-20 Term 2

1.

2.

3. Sample space:

Event of choosing a letter from to :

4.

(a) outcome(s)

(b) outcome(s)

(c) outcome(s)

5. coupon codes

6.

7.

8.

9.

12

160

, A , B , C , D , E FD F , D , E F

1238

862,488

13

(a)12

(b)1

13

(c)7

13

511


9. (a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the

probability of the event.

(b) Subtract.

(c) Select the answer that makes the sentence true.

10.

11.

12.

13. (a) How many ways can this be done, if the order of the choices is taken into consideration?

EventOutcomes

Probability1 2 3 4 5 6 7 8 9 10

X =P X7

10

not X =P not X3

10

=−1 P X3

10

is the same as .−1 P X ▼P(not X)

=P A1

70

=P B1

1680

96

12P 3 =1320

8C 4 =70


13. (a) How many ways can this be done, if the order of the choices is taken into consideration?

(b) How many ways can this be done, if the order of the choices is not taken into consideration?

14. (a) How many ways can this be done, if the order of the choices is relevant?

(b) How many ways can this be done, if the order of the choices is not relevant?

15.

16.

17.


12

6

60,480

84

(a) A certain committee consists of people. From the committee, a president, a vice-president, and a

treasurer are to be chosen. In how many ways can these offices be filled? Assume that a committee membercan hold at most one of these offices.

163

3360

(b) A pizza parlor has a choice of toppings for its pizzas. From these toppings, how many different -topping pizzas are possible?

11 11 8

165

60

0.11



Experiment Events Independent Dependent

A deck contains cards numbered through . A card is randomlyselected and reinserted into the deck. The deck is shuffled. Then anotherrandom selection is made.

Event A: The first

selection is a .

Event B: Thesecond selection is

a .

Rafael randomly selects a sock from a drawer containing black socks andbrown socks, and puts it on. Then another random selection is made fromthe remaining socks.

Event A: The firstselection is black.

Event B: Thesecond selection isbrown.

A family has two children.

Event A: The olderchild has red hair.

Event B: Bothchildren have redhair.

A number cube with sides labeled through is rolled twice.

Event A: The first

roll is a .

Event B: The

second roll is a .

A litter of puppies consists of black puppies and white puppies. A puppy israndomly selected and removed from the litter. Then another randomselection is made from the remaining puppies.

Event A: The firstselection is a whitepuppy.

Event B: Thesecond selection isa black puppy.

19.

20.

21.

22. Event " or ":

13 1 13 6

7

1 62

1

625

536

(a) What is the probability that the resident does not live alone?

______

(b) What is the probability that the resident does not own a car or does not live alone?

______

, 1 , 2 , 3 , 5 7 © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 12 Pr ac t i ce T es t #1 / 20

22. Event " or ":

Event " and ":

The complement of the event :

23. (a) Find the probabilities of the events below.

Write each answer as a single fraction.

(b) Select the probability that is equal to .

24. (a)

(b)

25. (a)

(b)

26.

A B , 1 , 2 , 3 , 5 7A B , 1 3

A , 4 , 5 , 6 , 7 8

=P A58

=P B9

16

=P A andB14

=P A orB1516

=+P A −P B P A and B1516

+P A −P B P A and B

P A and BP A

P B

P A or B

23

12

0.030.33


26.

27.

(a) Select all the clubs that Salma is a member of.Music Club

(b) How many students are members of the Spanish Club or the Computer Club (or both)?

students

(c) Which of these students are in only one club?Salma, Frank, Chau, and Lucy

28.

Hockey Football Basketball

Seventhgrade

Eighthgrade

29.

Swimming Baseball

Seventhgrade

Eighthgrade

30.

Probabilities Independent Dependent

; ; and =P A12 = P B

14 P A =B

18

; ;=P A13 = P B

16 = P B |A

12

; ;=P A12 = P B

16 = P A |B

12

; ;=P A16 = P B

14 = P A |B

15

9

13 7 15

6 12 12

11 8

6 10


30.

(a) P(parent)

(b) P(T-shirt and parent)

(c) P(T-shirt | parent)

31.

32.

(a)

(b)

33.

=0.5

=0.3

=0.6

(a) Find the probability that the patient showed improvement.

=P(improvement) 0.56

(b) Find the probability that the patient showed improvement, given that he took thenew medication.

P(improvement | new =medication) 0.55

(c) Is there evidence that a patient who takes the new medication is more likely toshow improvement than a randomly chosen patient from the group?

Yes, because the probability found in part (b) is much greater than theprobability found in part (a).

No, because the probability found in part (b) is much greater than theprobability found in part (a).

Yes, because the probability found in part (a) is much greater than theprobability found in part (b).

No, because the probability found in part (a) is much greater than theprobability found in part (b).

Yes, because the probability found in part (b) is about the same as theprobability found in part (a).

No, because the probability found in part (b) is about the same as theprobability found in part (a).

74 %

52 %

0.39


chapter 12 practice test #1 - m2...

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