Question

Probability -0.30 15: Suppose that at UVA, 76% of all undergraduates are in the College, 10% are in Engineering, 7% are in Commerce, 3% are in Nursing, and 4% are in Architecture. In each school, the per-centage of females is as follows: 55% in the College, 25% in Engineering, 49% in Commerce, 87% in Nursing, and 35% in Architecture. If a randomly selected student is male, what is the probability that he's from the College? Probability_

Answer 1

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Answer 2

M = male

F = female

P[M & college] = 76% * 45 %          = 34.20  % = X

P[M & engg] = 10% * 75 %             = 7.50 %

P[M & commerce] = 7% * 51 %       = 3.57 %

P[M & nursing] = 3% * 13%             = 0. 39%

P[M & architecture] = 4 % * 65 %    = 3.45%

P[M] = sum of the above =  49.11 %  = Y

P[college | M] = X / Y

= 34.20  / 49.11 

= 0.6963   ie 69.63 %