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临江仙 · 2020年08月16日

问一道题：NO.PZ2018122801000005

  1. FRM I
  2. Quantitative

问题如下：

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?

选项：

A.

1/4

B.

1/3

C.

1/2

D.

2/3

解释：

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

 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

这里英文是什么意思？

题目不是很懂

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品职答疑小助手雍 · 2020年08月16日

嗨，从没放弃的小努力你好：


贷款里有一半是次级的，一半的次级和四分之一的非次级满足XXX条件，问从贷款里选出来一个债符合XXX条件，问它是次级的概率是多少。

这种题完全不用懂英文，翻译过来就是总集里有，A和B各站50%，50%的A和25%的B满足XX条件，问总集里取一个样本满足XX条件，它是A的概率是多少？

满足XX条件的总共是1/4+1/8=3/8，A的占2/8，所以取一个样本符合XX条件的时候，它属于A的概率就是2/8除以3/8=2/3


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