Answer
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.