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文轩 · 2023年02月11日

看不太懂…..

NO.PZ2018122801000005

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

能中文翻译加讲解一下吗,principal balance exceeds在这里是什么啊

1 个答案
已采纳答案

DD仔_品职助教 · 2023年02月11日

嗨,从没放弃的小努力你好:


同学你好,

题目问:贷款里有一半是次级的,一半的次级和四分之一的非次级抵押贷款的本金余额超过了用作抵押品的财产价值,问从组合中随机选择一个抵押贷款进行审查,它的本金余额超过抵押品的价值,那么它是次级抵押贷款的概率是多少?

principal balance exceeds在这里就是一个条件,这种题完全不用懂英文,简化翻译一下就是总集里有,A和B各站50%,50%的A和25%的B满足XX条件(principal balance exceeds的条件),问总集里取一个样本满足XX条件,它是A的概率是多少?

总集里满足XX条件的是1/4+1/2*1/4=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比上3/8=2/3

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