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

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

游客2025-02-23  20
问题 In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that H will occur is 5.
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 D
解析 因为G、H是两个独立事件，所以P(G and H)=rs。Quantity A=P(G or H)-P(G and H)=(r+s-rs)-rs=r+s-2rs。由于0≤概率P≤1，所以0≤r≤1，0≤s≤1，则0≤rs≤1。当rs=0时，Quantity A=Quantity B；当rs＞0，Quantity A＜Quantity B。所以答案为D选项。
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