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albee · 2021年07月20日

解析中说到In this case, P(A/B)=0, because event A and B are mutually exclusive. P(A/B)为什么不是等于P(A)+P(B)?

  1. CFA I
  2. Quantitative

NO.PZ2015120604000067

问题如下：

Which of the following statements is the most correct?

选项：

A.

If events A and B are mutually exclusive, then P(A or B)=P(A)-P(B)

B.

If events A and B are mutually exclusive, then P(AB)=P(A)×P(B).

C.

If events A and B are mutually exclusive, then P(A or B)=P(A)+P(B)

解释：

C is correct.

P(AB)=P(A)×P(B) is only correct when A and B are independent events. In this case, P(A/B)=0,P(AB)=0，because event A and B are mutually exclusive

解析中说到In this case, P(A/B)=0, because event A and B are mutually exclusive. P(A/B)为什么不是等于P(A)+P(B)?

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星星_品职助教 · 2021年07月21日

同学你好，

P(A|B)是条件概率，意思是在B发生的前提下A发生的概率。由于A，B为互斥事件，所以B发生的前提下，A不可能发生，即P(A|B)=0.

🦦泡泡。 · 2021年07月20日

AB是互斥事件不可能同时发生 所以是0

albee · 2021年07月20日

P(A/B)不是只发生其中一个概率么？

🦦泡泡。 · 2021年07月21日

是条件概率～

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2022-10-01 11:21 1 · 回答

老师，我知道P（a|b）和P（ab）都得零，但是C咱们随便假设一下，如果说P（a）=0.3 P（b）=0.2 两个数一算最后也不得零啊 为什么选C呢？

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