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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
2024-01-12
31
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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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