According to a recent report 60 of US college graduates cann

According to a recent report, 60% of U.S. college graduates cannot find a full time job in their chosen profession. Assume 57% of the college graduates who cannot find a job are female and that 26% of the college graduates who can find a job are female. Given a male college graduate, find the probability he cannot find a full time job in his chosen profession?

Solution

Let

C = cannot find a full time job in their chosen profession

M, F = male, female

As by Bayes\' Rule,

P(M) = P(C) P(M|C) + P(C\') P(M|C\') = 0.60*(1-0.57) + (1-0.60)*(1-0.26) = 0.554

Hence,

P(C|M) = P(C) P(M|C) / P(M) = 0.60*(1-0.57)/0.554 = 0.465703971 [ANSWER]