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?
解析
D is correct.
考点 Bayes' formula
解析 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(A’) = 1/2, P(B|A) = 1/2, P(B|A’) = 1/4
P(A|B) = P(B|A)*P(A)/[P(B|A)*P(A) + P(B|A’)*P(A’)]
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
P(A’) 是什么？？？
我的理解是P(A|B)*P(B) = P(B|A)*P(A)，所以P(A|B) = P(B|A)*P(A)/P(B)，所以P(A|B) =40%。为什么解析里面是P(A|B) = P(B|A)*P(A)/[P(B|A)*P(A) + P(B|A’)*P(A’)]，[P(B|A)*P(A) + P(B|A’)*P(A’)]是什么？P(B|A’) 又是什么。。。
