Half of the mortgages in a portfolio are considered subprime. The principal balance of half of the subprime mortgages and one-quarter of the non-subprime mortgages exceeds the value of the property used as collateral. If you randomly select a mortgage from the portfolio for review and its principal balance exceeds the value of the collateral, what is the probability that it is a subprime mortgage?
A. 1/4
B. 1/3
C. 1/2
D. 2/3
Answer:D
Assume: A = event that the loan is subprime
B=event that the face value of the loan exceeds that the property
P(A) = 1/2
P(Ac) = 1/2
P(B|A) = 1/2
P(B|Ac) = 1/4
P(A|B) = P(B|A)*P(A)/[P(B|A)*P(A) + P(B|Ac)*P(Ac)]
P(A|B)= (1/2 * 1/2) / (1/2 * 1/2 + 1/4 * 1/2) = (1/4) / (1/4 + 1/8) = (1/4)/(3/8) = 8/12 = 2/3