Question

5% of men cheat on their wives at some point in their marriage. Of these cheaters, 50% of their wives could catch them by finding a piece of another woman’s clothing in their bedroom. Good husbands would only have another woman’s clothes somewhere in their bedroom (for some reason or another) 1% of the time. A wife finds an unknown underwear on her bed. How likely is the husband cheating?

Answer 1

Given,

P(Cheat) = 0.05

So P(Not cheat) = 1 - 0.05 = 0.95

P(Cloth | Cheat) = 0.50

P(Cloth | Not cheat) = 0.01

Hence by Baye's theorem:

P(Cheat | Cloth)

= 0.7246