Essentials of Statistics (5th Edition)

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

Chapter 4 - Probability - 4-5 Multiplication Rule: Complements and Conditional Probability - Page 173: 16


a) 0.4841 b)0.0000293 c)The detective is really lucky or amazingly good.

Work Step by Step

a) $P(at \ least \ one \ of \ them \ is \ cleared)=1−P(none \ of \ them \ is \ cleared)=1−(1−0.124)^{5}=1-0.876^{5}=0.4841$ b)$P(all \ cleared)=0.124^5=0.0000293 c) Because the probability in b) is really low, the detective is really lucky or amazingly good.
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