12-5 compound events course 1 warm up warm up lesson presentation lesson presentation problem of the...
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12-5 Compound Events
Course 1
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__
Course 1
12-5 Compound Events
Learn to list all the outcomes and find the theoretical probability of a compound event.
Course 1
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.
Course 1
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___
Course 1
12-5 Compound Events
Course 1
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