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
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
