Question

5. In some town, 51% of the adults are males and the other 49% are females. Someone held up the bank in town. Witnesses are certain the robber was smoking a cigar but did not see if the robber was a male or a female, we know that 9.5% of males smoke cigars and that 1.7% of females smoke cigars. Use Bayes' rule to find the probability that the robber was a male.

Answer 1

P(male | smokes cigar) = P(male and smokes cigar)/P(smokes cigar)

= 0.51x0.095/(0.51x0.095 + 0.49x0.017)

= 0.8533