Mutually exclusive events are events that have no outcomes in common.
Use the rule below to find the probability of mutually exclusive events.
P R O BA B I L I T Y O F M U T UA L LY E X C L U S I V E E V E N T S
For two mutually exclusive events A and B, the probability that either of the
events occurs is the sum of the probabilities of the events.
P(A or B) ⴝ P(A) ⴙ P(B)
Events A and B are mutually exclusive.
Finding the Probability of Mutually Exclusive Events
EXAMPLE 4
You are playing a game using the spinner at the
right, which is divided into equal parts. On your
spin, what is the probability that the spinner
lands on an even number or a prime number?
SOLUTION
First, find the probabilities of the events.
Let event A be getting an even number
and let event B be getting a prime number.
4
8
3
P(B) 8
P(A) 8
9
7
10
6
11
5
12
Of the 8 numbers, 4 are even.
Of the 8 numbers, 3 are prime.
Then find the sum of the probabilities.
4
8
3
8
7
8
P(A or B) 0.875
䉴
The probability that the spinner lands on an even number or a prime number is
0.875, or 87.5%.
..........
Overlapping events are events that have one or more outcomes in common.
Use the rule below to find the probability of overlapping events.
P R O BA B I L I T Y O F O V E R L A P P I N G E V E N T S
For two overlapping events A and B, the probability that either of the events
occurs is the sum of the probabilities of the events, minus the probability
that both events occur.
P(A or B) ⴝ P(A) ⴙ P(B) ⴚ P(A and B) Events A and B are overlapping.
Appendix 2
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