Let A denote the event that man reports that 5 occurs and E the event that 5 actually turns up.
∴ P(E) = and
Also, = Probability that man reports that 5 occurs given that 5 actually turns up = Probability of man speaking the truth =
= Probability that man reports that 5 occurs given that 5 doesnot turns up = Probability of man not speaking the truth =
∴ Required probability =