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陆佳莹 · 2021年08月22日

老师这道题似乎不能用画图方法解,那什么题型需要用到画图?什么题型需要用本题的解法?

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

老师这道题似乎不能用画图方法解,那什么题型需要用到画图?什么题型需要用本题的解法?可以帮忙总结一下么?我有点混乱。

2 个答案
已采纳答案

星星_品职助教 · 2021年08月23日

同学你好,

可以比较一下这道题目和上课例题讲的画图解的贝叶斯公式题目的区别。可以看出这道题给的是两个非条件概率,例如本题就是20% will fail 和70% receive a "good" rating。

而普遍的贝叶斯公式的题型(可以参照基础班讲义上的机器诊断和有病的那道题)是只给一个非条件概率,这个画在图像的第一支;然后再给一个条件概率,画在图像的第二支。这种题型才是用画图来解的。

-----

所以原则是能用画图的都直接画图,但两个非条件概率的题目我们直接用公式来解。

陆佳莹 · 2021年08月23日

星星解释的很清楚,赞一个👍

星星_品职助教 · 2021年08月23日

@陆佳莹 多谢,学习加油~

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