Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 4 - Probability - 4-3 Addition Rule - Beyond the Basics - Page 156: 43


a) $1−P(A)−P(B)+P\text{(A and B)}$. b) $1−P\text{(A and B)}$ c) No.

Work Step by Step

a) First must subtract the probability of getting A and the probability of getting B from $1$. However, if both A and B happen, we would count them twice, so we have to add back P(A and B). Thus, we find: $1−P(A)−P(B)+P\text{(A and B)}$. b) There are two possibilities: either you don't get A or you don't get B, or you get both. Thus, we find: $1−P\text{(A and B)}$ 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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