geometry unit 12 probability notes · geometry unit 12 probability notes 1 date name of lesson 12.1...

Geometry Unit 12 Probability Notes

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Date Name of Lesson

12.1 Representing Sample Spaces

12.2 Probability and Counting

12.4 Geometric Probability

12.5 Probability and the Multiplication Rule

12.6 Probability and the Addition Rule

12.7 Conditional Probability

12.8 Two-Way Frequency Tables


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12.1 Representing Sample Spaces

Example 1: Represent a Sample Space

One red token and one black token are placed in a

bag. A token is drawn, and the color is recorded. It is

then returned to the bag, and a second draw is made.

Represent the sample space for this experiment by

making an organized list, a table, and a tree diagram.

Create and Organized List

Create a Table

Create a Tree Diagram

Guided Practice 1: Represent a Sample Space

One yellow token and one blue token are placed in a

bag. A token is drawn and the color is recorded. It is

then returned to the bag and a second draw is made.

Choose the correct display of this sample space.

Create and Organized List

Create a Table

Create a Tree Diagram

Example 2:

Multistage Tree Diagrams

CHEF’S SALAD A chef’s salad at a local restaurant

comes with a choice of French, ranch, or blue cheese

dressings and optional toppings of cheese, turkey, and

eggs. Draw a tree diagram to represent the sample

space for salad orders.

Draw a tree diagram with 4 stages.

The sample space is the result of 4 stages.

● Dressing (F, R, or BC)

● Cheese (C or NC)

● Turkey (T or NT)

● Eggs (E or NE)


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Use the Fundamental Counting Principal

CARS New cars are available with a wide selection

of options for the consumer. One option is chosen

from each category shown. How many different cars

could a consumer create in the chosen make and

model?

BICYCLES New bicycles are available with a wide

selection of options for the rider. One option is

chosen from each category shown. How many

different bicycles could a consumer create in the

chosen model?


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12.2 Probability and Counting

Example 1: Find the Union of Events

A set of 12 cards are numbered 1 through 12. You

choose one card at random. Let A be the event that

you choose a multiple of 4. Let B be the event that

you choose a number less than 3.

Find A ∪ B

Find the probability that event A or event B will

occur.

Example 2: Find the Intersection of Events

The Venn diagram shows the employees of a store

and the days of the weekend when they work. Let A

be the event that an employee works Saturday and let

B be the event that an employee works Sunday. An

employee is chosen at random to attend a training

session.

Find A ∩ B What is the probability that the employee who is

chosen works on both Saturday and Sunday?


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Example 3: Use Complementary Events

A box contains 35 red marbles and 120 marbles

of other colors. Isaac chooses one of the marbles

without looking. What is the probability that he

does not choose a red marble?

Example 4: Find Probabilities of Events

Some visitors to an amusement park were surveyed to find

out whether they rode the roller coaster or the Ferris

wheel. The Venn diagram represents the results of the

survey. One respondent will be chosen at random to win a

free pass to the park. Find the probability that the winner

will be someone who rode the roller coaster and the Ferris

wheel.


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12.4 Geometric Probability

Example 1: Lengths and Geometric Probability

Point Z is chosen at random on AD. Find the

probability that Z is on AB.

Guided Practice 1: Length Probabilities

Point R is chosen at random on LO. Find the

probability that R is on MN.

Example 2:

Halley’s Comet orbits Earth every

76 years. What is the probability that Halley’s Comet

will complete an orbit within the next decade?

Example 2B: Translations in a Coordinate Plane

SUBWAY You are in the underground station

waiting for the next subway car, and are unsure how

long ago the last one left. You do know that the

subway comes every sixteen minutes. What is the

probability that you will get picked up in the next

12 minutes?


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Example 3: Area and Geometric Probability

DARTS The targets of a dartboard are formed by

3 concentric circles. If the diameter of the center

circle is 4 inches and the circles are spread

3 inches apart, what is the probability that a

player will throw a dart into the center circle?

Guided Practice 3:

RING TOSS If at a carnival,

you toss a ring and it lands in

the red circle shown below,

then you win a prize. The

diameter of the circle is 4 feet.

If the dimensions of the blue

table are 8 feet by 5 feet, what

is the probability if the ring is

thrown at random that you will

win a prize?

Example 4: Angle Measure Probability

Use the spinner to find

the P (pointer landing

on section 3).

Use the spinner to find

the P (pointer landing

on section 1).

Guided Practice 4:

Use the spinner to find the

P (pointer landing on

section C).

Use the spinner to find the

P (pointer landing on

section E).


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12.5 Probability and the Multiplication Rule

Independent Events:

Dependent Events:

Example 1:

Determine whether the event is independent or

dependent. Explain your reasoning.

A. Anna rolls a 6 on one number cube and a 3 on

another cube.

B. A queen is selected from a standard deck of cards and not put back. Then a king is selected.

Guided Practice 1:

Determine whether the event is independent or

dependent. Explain your reasoning.

A. A marble is selected from a bag. It is not put back.

Then a second marble is selected.

B. A marble is selected from a bag. Then a card is

selected from a deck of cards.

Example 2:

A bag contains a white marble, a blue marble, a

yellow marble, and a green marble. Andrew selects

the white marble, replaces it, and then selects the

green marble.

Are these events independent?

Explain using probability.


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Guided Notes:

EATING OUT Michelle and Christina are going out to lunch. They put 5 green slips of paper and 6 red slips

of paper into a bag. If a person draws a green slip, she will order a hamburger. If she draws a red slip, she will

order pizza. Michelle will draw first and put her slip back. Then Christina will draw. What is the probability

that both girls draw green slips?

Your Turn:

LABS In Science class, students are drawing marbles out of a bag to determine lab groups. There are 4 red

marbles, 6 green marbles, and 5 yellow marbles left in the bag. Jacinda draws a marble, but not liking the

outcome, she puts it back and draws a second time. What is the probability that each of her 2 draws gives her

a red marble?


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GAMES At the school carnival, winners in the ringtoss game are randomly given a prize from a bag that

contains 4 sunglasses, 6 hairbrushes, and 5 key chains.

The first three players all win prizes. Find each probability.

A. P (sunglasses, hairbrush, key chain)

B. P (hairbrush, hairbrush, not a hairbrush)

LABS In Science class, students are again drawing marbles out of a bag to determine lab groups. There are 4

red marbles, 6 green marbles, and

5 yellow marbles. This time Graham draws a marble and does not put his marble back in the bag. Then his

friend Meena draws a marble. What is the probability they both draw green marbles?

Davina’s family will cancel their weekend camping trip if the probability of rain on both Saturday and Sunday

is greater than 10%. According to the weather forecast, there is a 30% chance of rain on Saturday and a 20%

chance of rain on Sunday. Assuming the two events (rain on Saturday and rain on Sunday) are independent,

should Davina’s family cancel the trip? Justify your answer using probability

Find the probability of rain on Saturday and Sunday.

Should Davina’s family cancel their weekend trip?


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12.6 Probability and the Addition Rule

Mutual Exclusive Events:

Not Mutually Exclusive Events:

Example 1A

CARDS Han draws one card from a standard deck.

Determine whether drawing an ace or a 9 is mutually

exclusive or not mutually exclusive. Explain your

reasoning.

Example 1B

CARDS Han draws one card from a standard deck.

Determine whether drawing a king or a club is

mutually exclusive or not mutually exclusive. Explain

your reasoning.

Your Turn 1A

A. For a Halloween grab bag, Mrs. Roth has thrown

in 10 caramel candy bars, 15 peanut butter candy

bars, and 5 apples to have a healthy option.

Determine whether drawing a candy bar or an apple

is mutually exclusive or not mutually exclusive.

Your Turn 2A

B. For a Halloween grab bag, Mrs. Roth has thrown

in 10 caramel candy bars, 15 peanut butter candy

bars, and 5 apples to have a healthy option.

Determine whether drawing a candy bar or something

with caramel is mutually exclusive or not mutually

exclusive.

Example 2:

COINS Trevor reaches into a can that contains 30

quarters, 25 dimes, 40 nickels, and 15 pennies. What

is the probability that the first coin he picks is a

quarter or a penny?

Your Turn 2:

MARBLES Hideki collects colored marbles so he

can play with his friends. The local marble store has a

grab bag that has 15 red marbles, 20 blue marbles, 3

yellow marbles and 5 mixed color marbles. If he

reaches into a grab bag and selects a marble, what is

the probability that he selects a red or a mixed color

marble?


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Example 3:

ART Use the table below. What is the probability

that Namiko selects an acrylic or a still life?

Your Turn 3:

SPORTS Use the table. What is the probability that

if a high school athlete is selected at random that the

student will be a sophomore or a basketball player?


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12.7 Conditional Probability

Example 1

Mr. Monroe is organizing the gym class into two teams for a game. The 20 students randomly draw cards

numbered with consecutive integers from 1 to 20.

• Students who draw odd numbers will be on the Red team.

• Students who draw even numbers will be on the Blue team.

If Monica is on the Blue team, what is the probability that she drew the number 10?

Your Turn 1

Mr. Riley’s class is traveling on a field trip for Science class. There are two busses to take the students to a

chemical laboratory. To organize the trip, 32 students randomly draw cards numbered with consecutive

integers from 1 to 32.

• Students who draw odd numbers will be on the first bus.

• Students who draw even numbers will be on the second bus.

If Yael will ride the second bus, what is the probability that she drew the number 18 or 22?

Example 2

At a fruit stand, 24% of the grape bags have red grapes, 15% have black grapes, and 3% have both red and

black grapes. A customer selects a bag at random.

A. What is the probability that the bag contains red grapes, given that it contains black grapes?

B. What is the probability that the bag contains black grapes, given that it contains red grapes?


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Your Turn 2

LABS In Science class, students are drawing marbles out of a bag to determine lab groups. There are 4 red

marbles, 6 green marbles, and 5 yellow marbles left in the bag. Jacinda draws a marble, but not liking the

outcome, she puts it back and draws a second time. What is the probability that each of her 2 draws gives her

a red marble?

Example 3

PETS A survey of Kingston High School students found that 63% of the students had a cat or a dog for a pet.

If two students are chosen at random from a group of 100 students, what is the probability that at least one of

them does not have a cat or a dog for a pet?

Your Turn 3

LABS In Science class, students are again drawing marbles out of a bag to determine lab groups. There are 4

red marbles, 6 green marbles, and 5 yellow marbles. This time Graham draws a marble and does not put his

marble back in the bag. Then his friend Meena draws a marble. What is the probability they both draw green

marbles?


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12.8 Two-Way Frequency Tables

Example 1

Valerie asks a random sample of 70 science teachers and math teachers whether they have been to the town’s

planetarium. She finds that 25 science teachers have been to the planetarium and 3 have not, while 20 math

teachers have been to the planetarium and 22 have not. Make a two-way frequency table to organize the data.

Example 2

Joint Frequency:

Marginal Frequency:

A. How many customers at Donna’s Diner paid by credit card? Is the frequency marginal or joint?

B. How many customers paid by cash? Is the frequency marginal or joint?


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Example 3

Convert the below table to a table of relative frequencies.

Example 4

Use the below relative frequency table to determine whether paying by cash or credit card is independent of

the restaurant. Explain.

Example 5

Use the relative frequency table above to find the probability that a customer pays by cash, given that he or

she eats at Joe’s Palace.

geometry unit 12 probability notes · geometry unit 12 probability notes 1 date name of lesson 12.1...

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