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.

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.