9-3 Sample Spaces

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

9-3 Sample Spaces

Warm Up

1. A dog catches 8 out of 14 flying disks thrown. What is the experimental probability that it will catch the next one?

2. If Ted popped 8 balloons out of 12 tries, what is the experimental probability that he will pop the next balloon?

47

23

9-3 Sample Spaces

Problem of the Day

How many different types of meat pizzas can be made if the choices of meat topping are pepperoni, sausage, ham, and meatball? (Hint: There can be 1, 2, 3, or 4 toppings on the pizza.)

15 (4 one-topping, 6 two-topping, 4 three-topping, and 1 four-topping)

9-3 Sample Spaces

MA.7.P.7.1 Determine the outcome of an experiment…

Sunshine State Standards

9-3 Sample Spaces

Vocabulary

sample spaceFundamental Counting Principle

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3

2

6

3

2

6

Because you can roll the numbers 1, 2, 3, 4, 5, and 6 on a number cube, there are 6 possible outcomes. Together, all the possible outcomes of an experiment make up the sample space.

You can make an organized list to show all possible outcomes of an experiment.

9-3 Sample Spaces

One bag has a red tile, a blue tile, and a green tile. A second bag has a red tile and a blue tile. Vincent draws one tile from each bag. What are all the possible outcomes? How many outcomes are in the sample space?

Additional Example 1: Problem Solving Application

9-3 Sample Spaces

11 Understand the Problem

Rewrite the question as a statement.

• Find all the possible outcomes of drawing one tile from each bag, and determine the size of the sample space.

List the important information:

• There are two bags.

• One bag has a red tile, a blue tile, and a green tile.

Additional Example 1 Continued

• The other bag has a red tile and a blue tile.

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22 Make a Plan

You can make an organized list to show allpossible outcomes.

Additional Example 1 Continued

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Solve33

Let R = red tile, B = blue tile, and G = green tile.

Record each possible outcome.

The possible outcomes are RR, RB, BR, BB, GR, and GB. There are six possible outcomes in the sample space.

Additional Example 1 Continued

BG

RG

BB

RB

BR

RR

Bag 2Bag 1

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Look Back44

Each possible outcome that is recorded in the list is different.

Additional Example 1 Continued

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Check It Out: Example 1

Darren has two bags of marbles. One has a green marble and a red marble. The second bag has a blue and a red marble. Darren drawsone marble from each bag. What are all the possible outcomes? How many outcomes are in the sample space?

The four possible outcomes are GB, GR, RB, and RR. There are four possible outcomes in the sample space.

9-3 Sample Spaces

There are 4 cards and 2 tiles in a board game. The cards are labeled N, S, E, and W. The tiles are numbered 1 and 2. A player randomly selects one card and one tile. What are all the possible outcomes? How many outcomes are in the sample space?

Additional Example 2: Using a Tree Diagram to Find a Sample Space

Make a tree diagram to show the sample space.

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Check It Out: Example 2

Shauna spins the spinner at left and flips a coin. Complete the tree diagram. What are all the possible outcomes? How many outcomes are in the sample space?

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Check It Out: Example 2 Continued

1

H T

2

H T

3

H T

4

H T

The possible outcomes are 1H, 1T, 2H, 2T, 3H, 3T, 4H, and 4T. There are eight possible outcomes.

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In Additional Example 1, there are three outcomes for the first bag and two outcomes for the second bag.

In Additional Example 2, there are four outcomes for the cards and two outcomes for the tiles. Cards Tiles

First bag Second bag

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The Fundamental Counting Principle states that you can find the total number of outcomes for two or more experiments by multiplying the number of outcomes for each separate experiment.

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Carrie rolls two 1–6 number cubes. How many outcomes are possible?

Additional Example 3: Application

The first number cube has 6 outcomes.

The second number cube has 6 outcomes

List the number of outcomes for each separate experiment.

6 · 6 = 36

There are 36 possible outcomes when Carrie rollstwo 1–6 number cubes.

Use the Fundamental Counting Principle.

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Check It Out: Example 3A

Juan tosses a coin and rolls a number cube. How many outcomes are possible?

There are two possible outcomes for the coin. There are six possible outcomes for the number cube.

2 × 6 = 12

There are twelve possible outcomes.

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Check It Out: Example 3B

Juan rolls a number cube and spins the spinner shown in Check It Out question 2. How many outcomes are possible?

There are six possible outcomes for the number cube. There are four possible outcomes for the spinner.

6 × 4 = 24

There are 24 possible outcomes.

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Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

9-3 Sample Spaces

Lesson Quiz

What are all the possible outcomes? How many outcomes are in the sample space?

1. a three question true-false test

2. tossing four coins

3. choosing a pair of cocaptains from the following athletes: Anna, Ben, Carol, Dan, Ed, Fran

8 possible outcomes: TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF

16 possible outcomes: HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT,THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT

15 possible outcomes: AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF

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1. Three fair coins are tossed. What are all the possible outcomes? How many outcomes are in the sample space?

A. 2 possible outcomes: H, T

B. 4 possible outcomes: HH, HT, TH, TT

C. 6 possible outcomes: HHH, HHT, HTT, THH, TTH, TTT

D. 8 possible outcomes: HHH, HHT, HTT, HTH, THH, THT, TTH, TTT

Lesson Quiz for Student Response Systems

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2. Sam tosses a coin and rolls a number cube. What are all the possible outcomes? How many outcomes are in the sample space? A. 8 possible outcomes: H, T, 1, 2, 3, 4, 5, 6

B. 12 possible outcomes: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

C. 12 possible outcomes: HH, HT, TH,TT, 12, 23, 34, 45, 56, 61, 11, 66

D. 24 possible outcomes: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6, 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T

Lesson Quiz for Student Response Systems

9-3 Sample Spaces

3. Bag A contains a red, a blue, and a yellow ball. Bag B contains a white, an orange, and a green ball. Frederica draws one ball from each bag. What are all the possible outcomes? How many outcomes are in the sample space?

A. 9 possible outcomes: RW, RO, RG, BW, BO, BG, YW, YO, YG

B. 9 possible outcomes: RR, BB, YY, WW, OO, GG, RW, BO, YG

C. 6 possible outcomes: RR, RO, RY, WW, WO, WG

Lesson Quiz for Student Response Systems