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勇往直前 · 2021年12月11日

为什么不是5%*50%*30%

  1. CFA I
  2. Quantitative

NO.PZ2021062201000006

问题如下：

In a typical year, 5% of all CEOs are fired for "performance" reasons. Assume that CEO performance is judged according to stock performance and that 50% of stocks have above-average returns or "good" performance. Empirically, 30% of all CEOs who were fired had "good" performance.

Using Bayes' formula, what is the probability that a CEO will be fired given "good" performance? (Hint, let P(A) be the probability of a CEO being fired, P(B) be the probability of a "good" performance rating, P(B I A) be the likelihood of a "good" performance rating given that the CEO was fired, and P(A I B) be the likelihood of the CEO being fired given a "good" performance rating.)

选项：

A.

1.5%

B.

2.5%

C.

3.0%

解释：

C is correct. With Bayes' formula, the probability of the CEO being fired given a "good" rating is：

P(A∣B)=P(B∣A)P(B)P(A)P(A|B) = \frac{{P(B|A)}}{{P(B)}}P(A)

where

P(A) = 0.05 = probability of the CEO being fired

P(B) = 0.50 = probability of a "good" rating

P(B | A) = 0.30 = probability of a "good" rating given that the CEO is fired

With these estimates, the probability of the CEO being fired given a "good" rating is：

P(A∣B)=P(B∣A)P(B)P(A)=0.30.5×0.05=0.03P(A|B) = \frac{{P(B|A)}}{{P(B)}}P(A) = \frac{{0.3}}{{0.5}} \times 0.05 = 0.03

Although 5% of all CEOs are fired, the probability of being fired given a "good" performance rating is 3%.

知识点：Probability Concepts-Bayes' Formula

为什么不是5%*50%*30%再除以第一个条件，这个计算和视频课中的做法不一样。真的很困惑，麻烦老师帮忙。谢谢
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1 个答案

星星_品职助教 · 2021年12月11日

同学你好，

视频中讲的是画图的做法。画图法的前提是：给出一个非条件概率和一个条件概率

而这道题给出的是两个非条件概率，所以需要套用公式来做。

按照讲义上的这个公式，代入题干中给出的A、B，就可以解题。公式右侧的三项内容题干中都是直接给出的。


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