Essentials of Statistics (5th Edition)

Published by Pearson
ISBN 10: 0-32192-459-2
ISBN 13: 978-0-32192-459-9

Chapter 4 - Probability - 4-3 Addition Rule - Page 156: 43

Answer

a. $1-P(A)-P(B)+P(A\ and\ B)$ b. $1-P(A\ and\ B)$ c. No

Work Step by Step

a. We first must subtract the probability of getting A and the probability of getting B from 1. However, if both A and B occurred, we would be counting twice, so we have to add back $P(A\ and\ B)$. Thus, we find: $1-P(A)-P(B)+P(A\ and\ B)$. b. There are two options: either you don't get A or you don't get B, or you get both. Thus, we find: $1-P(A\ and\ B)$ c. They are not equal, for the probability that you don't get either is not equal to the probability that you don't get at least one of them.
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