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呆呆兽 · 2023年01月31日

Probability Concepts

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?



A不正确Less than 25

B

25

C

More than 25



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

1 红色部分解析看不太懂 为什么标准2是非相互独立时间,概率B为0.5时,A在B条件下发生的概率就大于0.5?

2 the contingent probability 这个概念是什么意思。



1 个答案

星星_品职助教 · 2023年01月31日

同学你好,

1)这里的非独立性指的是题干中的正相关(positively related)。由于正相关,所以当B发生时,A也会同时发生,即A发生的概率增加,也就要大于原来的P(A)=0.5;

2)contingent probability就是条件概率,也就是P(A|B),一般使用conditional probability更多一些。

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