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LESSON
Name
Date
11.8 Study Guide
For use with pages 626–632
GOAL
Find the probability that event A or event B occurs.
VOCABULARY
Disjoint events, or mutually exclusive events, are events that have
no outcomes in common. Overlapping events are events that have
one or more outcomes in common.
Two events are complementary events if they are disjoint events and
one event or the other must occur.
EXAMPLE
1 Identifying Disjoint and Overlapping Events
Tell whether the events are disjoint or overlapping.
a. Randomly select a number from
b. Randomly select a card from a
1 to 20.
52-card deck.
Event A: Select an even number.
Event A: Select an Ace.
Event B: Select a number less than 2.
Event B: Select a Club.
EXAMPLE
Solution
a. The outcomes for event A are 2, 4, 6,
8, 10, 12, 14, 16, 18, and 20. The
outcome for event B is 1. There are
no outcomes in common.
b. Because one card is an Ace of Clubs,
the events have an outcome in common.
Answer: The events are disjoint.
Answer: The events are overlapping.
2 Finding the Probability of Disjoint Events
Lesson 11.8
A bag of marbles contains 25 yellow marbles, 40 red marbles, 5 purple marbles,
and 30 blue marbles. You randomly draw a marble from the bag. What is the
probability that you draw a yellow or a purple marble?
Solution
The events are disjoint because the marble cannot be both yellow and purple.
Event A: You choose a yellow marble.
Event B: You choose a purple marble.
P(A or B) ⫽ P(A) ⫹ P(B)
25
5
100
100
30
3
⫽ ᎏᎏ ⫽ ᎏᎏ
100
10
⫽ ᎏᎏ ⫹ ᎏᎏ
Probability of disjoint events
Substitute probabilities.
Add. Then simplify.
3
10
Answer: The probability that you draw either a yellow or a purple marble is ᎏᎏ.
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
Chapter 11
Pre-Algebra
Resource Book
75
j9rb-1108.qxd 11/13/03 1:50 PM Page 76
LESSON
Name
Date
11.8 Study Guide
Continued
EXAMPLE
For use with pages 626–632
3 Finding the Probability of Overlapping Events
You randomly choose a number from 1 to 30. What is the probability that you
choose a prime number or a number greater than 20?
Solution
There are 10 prime numbers from 1 to 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Two of these prime numbers are greater than 20. There are 10 numbers greater
than 20 but less than or equal to 30.
Event A: The number is prime.
Event B: The number is greater than 20.
P(A or B) ⫽ P(A) ⫹ P(B) ⫺ P(A and B)
10
30
10
30
2
30
3
5
⫽ ᎏᎏ ⫹ ᎏᎏ ⫺ ᎏᎏ ⫽ ᎏᎏ
Probability of overlapping events
Substitute probabilities. Then simplify.
Answer: The probability that you choose a prime number or a number greater
3
5
than 20 is ᎏᎏ.
Exercises for Examples 1–3
You randomly choose a number from 1 to 20. For the specified events A and B,
tell whether the events are disjoint or overlapping. Then find P(A or B).
1. Event A: Choose a number divisible by 5.
Event B: Choose a number divisible by 3.
Lesson 11.8
2. Event A: Choose a number divisible by 12.
Event B: Choose a number divisible by 5.
EXAMPLE
4 Finding the Probability of Complementary Events
1
You spin a spinner. The probability that you spin red is ᎏᎏ. What is the probability
3
that you do not spin red?
Solution
The events red and not red are complementary events because they are disjoint
and one or the other must occur.
P(not red) ⫽ 1 ⫺ P(red)
1
3
2
3
⫽ 1 ⫺ ᎏᎏ ⫽ ᎏᎏ
Probability of complementary events
1
3
Substitute ᎏᎏ for P(red). Then subtract.
2
3
Answer: The probability that you do not spin red is ᎏᎏ, or about 66.67%.
Exercises for Example 4
Given P(A), find P(not A).
3. P(A) ⫽ 44%
76
Pre-Algebra
Chapter 11 Resource Book
4. P(A) ⫽ 0.01
6
7
5. P(A) ⫽ ᎏᎏ
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.