12-5 Compound Events

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpA game die with eight sides numbered 1 through 8 is rolled. Find each probability.

1. P(1, 2, or 3)

2. P(even number)

3. P(number greater than 9)

38__

12__

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12-5 Compound Events

Problem of the Day

Sam and Pam can have an apple, an orange, or a pear. What is the probability that they will pick the same snack?13__

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12-5 Compound Events

Learn to list all the outcomes and find the theoretical probability of a compound event.

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12-5 Compound Events

Vocabulary

compound event

Insert Lesson Title Here

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12-5 Compound Events

A compound event consists of two or more single events. For example, the birth of one child is a single event. The births of four children make up a compound event.

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12-5 Compound Events

Additional Example 1A: Finding Probabilities of Compound Events

Jerome spins the spinner and rolls a fair number cube.

Find the probability that the number cube will show an even number and that the spinner will show a B.

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12-5 Compound Events

Additional Example 1A Continued

1 2 3 4 5 6

A 1, A 2, A 3, A 4, A 5, A 6, A

B 1, B 2, B 3, B 4, B 5, B 6, B

C 1, C 2, C 3, C 4, C 5, C 6, C

Number Cube

Spinner

First find all of the possible outcomes.

There are 18 possible outcomes, and all are equally likely.

Three of the outcomes have an even number and B: 2, B; 4, B; and 6, B.

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12-5 Compound Events

Additional Example 1A Continued

P(even, B)= 18 possible outcomes ____________________3 ways events can occur

= 3

18___

=1

6__ Write your answer in simplest

form.

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12-5 Compound Events

Additional Example 1B: Finding Probabilities of Compound Events

Find the probability that the number cube showing 4 and the spinner showing A.

Only one outcome is 4, A.

P(4, A)= 18 possible outcomes ____________________ 1 way event can occur

= 1

18___

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12-5 Compound Events

Additional Example 1C: Finding Probabilities of Compound Events

In the experiment proposed in the student book, what is the probability of the coin showing tails, the spinner showing purple, and a green marble being chosen?

There are 18 equally likely outcomes.

P(tails, purple, green)= 18 possible outcomes____________________ 1 way event can occur

= 1

18___

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12-5 Compound Events

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12-5 Compound Events

You could also use the Fundamental Counting Principle to find the total possible outcomes.

coin • spinner • marble 2 • 3 • 3 = 18 total outcomes

Remember!

Check It Out: Example 1A

Kiki spins the spinner and rolls a fair number cube.

Find the probability of the number cube showing an odd number and the spinner showing A.

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12-5 Compound Events

Check It Out: Example 1A Continued

1 2 3 4 5 6

A 1, A 2, A 3, A 4, A 5, A 6, A

B 1, B 2, B 3, B 4, B 5, B 6, B

C 1, C 2, C 3, C 4, C 5, C 6, C

Number Cube

Spinner

First find all of the possible outcomes.

There are 18 possible outcomes, and all are equally likely.

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12-5 Compound Events

Three of the outcomes have an odd number and BA: 1, A; 3, A; and 5, A.

P(odd, A)= 18 possible outcomes ____________________3 ways events can occur

= 3

18___

=1

6__ Write your answer in simplest

form.

Check It Out: Example 1A Continued

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12-5 Compound Events

Check It Out: Example 1B

Find the probability of the number cube showing 6 and the spinner showing C.

Only one outcome is 6, C.

P(6, C)= 18 possible outcomes ____________________ 1 way event can occur

= 1

18___

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12-5 Compound Events

Check It Out: Example 1C

In a similar experiment, what is the probability of two coins showing heads, and a red marble being chosen from a bag of marbles consisting of 1 red, 1 green, and 1 blue?

There are 12 equally likely outcomes.

P(heads, heads, red)= 12 possible outcomes____________________ 1 way event can occur

= 1

12___

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12-5 Compound Events

Lesson QuizAn experiment involves one spin of the spinner and one flip of the coin. Find each probability.

1. What is the probability of the spinner landing on red and the coin landing tails up?

2. What is the probability of the spinner landing on an odd number and the coin landing heads up?

3. What is the probability of the spinner landing on an even number and the coin landing tails up?

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12-5 Compound Events