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vee · 2022年11月26日

做对了但是想提问

NO.PZ2021062201000005

问题如下:

An analyst estimates that 20% of high-risk bonds will fail (go bankrupt). If she applies a bankruptcy prediction model, she finds that 70% of the bonds will receive a "good" rating, implying that they are less likely to fail. Of the bonds that failed, only 50% had a "good" rating.

Use Bayes' formula to predict the probability of failure given a "good"rating. (Hint, let P(A) be the probability of failure, P(B) be the probability of a "good" rating, P(B | A) be the likelihood of a "good" rating given failure, and P(A | B) be the likelihood of failure given a "good" rating.)

选项:

A.

5.7%

B.

14.3%

C.

28.6%

解释:

B is correct. With Bayes' formula, the probability of failure given a "good"rating is:

P(AB)=P(BA)P(B)P(A)P(A|B) = \frac{{P(B|A)}}{{P(B)}}P(A)

where

P(A) = 0.20 = probability of failure

P(B) =0.70 = probability of a "good" rating

P(B | A) =0.50 = probability of a "good" rating given failure

With these estimates, the probability of failure given a "good" rating is:

P(AB)=P(BA)P(B)P(A)=0.50.7×0.20=0.143P(A|B) = \frac{{P(B|A)}}{{P(B)}}P(A) = \frac{{0.5}}{{0.7}} \times 0.20 = 0.143

If the analyst uses the bankruptcy prediction model as a guide, the probability of failure declines from 20% to 14.3%.

知识点:Probability Concepts-Bayes' Formula

 implying that they are less likely to fail. 这句话是什么意思,干扰项吗

1 个答案

星星_品职助教 · 2022年11月26日

同学你好,

这半句话是对前面的good rating的一个附加解释,说的是good rating就意味着这只债券违约的可能性小。

从解题的角度出发,这半句话没用。

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