In a probability experiment, G and H are independent events. The probability tha

游客2025-02-23 18

问题 In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that //will occur is s, where both r and s are greater than 0.
Quantity A: The probability that either G or H will occur, but not both
Quantity B: r+s-rs

选项 A、Quantity A is greater.
B、Quantity B is greater.
C、The two quantities are equal.
D、The relationship cannot be determined from the information given.

答案 B

解析这道题是一道很简单的集合/概率的题目，解题用到的是交并集公式，P(G∪H)=P(G)+P(H)=P(G∩H)。当然，注意到Quantity A中提到了“but not both”，所以需要在上面这个公式的基础上再减掉一个P(G∩H)。因为P(G∪H)本身指的是“The probability that either G or H will occur (including both)”。所以Quantity A=r+s-rs-rs=r+s-2rs。比较Quantity B，可以得知，Quantity A＜Quantity B。

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