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Scarle · 2022年09月15日

看不懂题，能翻译一下问题和答案吗？谢谢

  1. CFA I
  2. Quantitative

NO.PZ2021062201000001

问题如下：

Elorence Hixon is screening a set of 100 stocks based on two criteria (Criterion1 and Criterion 2). She set the passing level such that 50% of the stocks passed each screen. For these stocks, the values for Criterion 1 and Criterion 2 are not independent but are positively related. How many stocks should pass Hixon's two screens?

选项：

A.

Less than 25

B.

25

C.

More than 25

解释：

C is correct.

Let event A be a stock passing the first screen (Criterion 1) and event B be a stock passing the second screen (Criterion 2). The probability of passing each screen is P(A) = 0.50 and P(B) = 0.50. If the two criteria are independent, the joint probability of passing both screens is P(AB) =P(A)P(B)=0.50 × 0.50 = 0.25, so 25 out of 100 stocks would pass both screens. However the two criteria are positively related, and P(AB) ≠ 0.25. Using the multiplication rule for probabilities, the joint probability of A and B is P(AB) = P(A I B) P(B).

If the two criteria are not independent, and if P(B) = 0.50, then the contingent probability of P(A | B) is greater than 0.50. So the joint probability of P(AB)=P(A | B) P(B) is greater than 0.25. More than 25 stocks should pass the two screens.

知识点：Probability Concepts

看不懂题，能翻译一下问题和答案吗？谢谢

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2 个答案

星星_品职助教 · 2023年07月30日

@Nickyan

根据的就是“由于此时标准1和标准2是positive related，所以如果标准2发生，会增加标准1发生的概率”。

标准2就是B，标准1就是A。P(A I B)是在B发生的条件下，A发生的概率。

目前已知B（通过标准2）发生了，B发生对A（通过标准1）还有正向的影响（positive related）。所以在B发生的条件下A发生的概率P(A I B)就要大于A自己单独发生的概率P(A)。

星星_品职助教 · 2022年09月15日

同学你好，

题干大意为：Hixon在根据两条标准从100只股票中选股。每只股票通过标准1和标准2筛选的概率都为50%。如果标准1和标准2不是相互独立，而是有正向关系的话，有多少股票可以同时通过这两条标准的筛选。

解：设一只股票通过标准1筛选的概率为P(A)，通过标准2筛选的概率为P(B)。根据题意可知，P(A)=P(B)=50%。

则要计算的是P(AB)，根据乘法法则， P(AB) = P(A I B)* P(B).

如果标准1和标准2相互独立，则P(AB) = P(A )* P(B)=50%*50%=25%。

由于此时标准1和标准2是positive related，所以如果标准2发生，会增加标准1发生的概率，也就是P(A I B)＞P(A )=50%.

所以P(AB) = P(A I B) *P(B)大于P(AB) = P(A )* P(B)，后者等于25%。

即100只股票中，同时通过两个标准的股票数目大于25只。

Nickyan · 2023年07月28日

由于此时标准1和标准2是positive related，所以如果标准2发生，会增加标准1发生的概率，也就是P(A I B)＞P(A )=50%. 请问P(A I B)＞P(A )=50%.是哪个方程得出来的

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