Suppose that at UVA 74 of all undergraduates are in the Coll

Suppose that at UVA, 74% of all undergraduates are in the College, 10% are in Engineering, 6% are in Commerce, 5% are in Nursing, and 5% are in Architecture. In each school, the percentage of females is as follows: 56% in the College, 27% in Engineering, 46% in Commerce, 87% in Nursing, and 34% in Architecture. If a randomly selected student is male, what is the probability that he\'s from the College?

Solution

P(Col|M) = P(Col) P(M|Col) / P(M)

Here,

P(M) = P(Col) P(M|Col) + P(Eng) P(M|Eng) + P(Com) P(M|Com) + P(Nur) P(M|Nur) + P(Arc) P(M|Arc)

P(M) = 0.74*(1-0.56) + 0.10*(1-0.27) + 0.06*(1-0.46) + 0.05*(1-0.87) + 0.05*(1-0.34)

P(M) = 0.4705

Thus,

P(Col|M) = P(Col) P(M|Col) / P(M) = 0.74*(1-0.56)/0.4705

= 0.692029756 [ANSWER]