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Ethan橙 · 2023年09月16日

P(AB)和P(A∩B)有区别么

  1. FRM I
  2. Quantitative

NO.PZ2020010301000017

问题如下：

Based on the probabilities in the diagram below, considering the three distinct pairs of events, how many of these pairs are independent?





选项：

A.

0

B.

1

C.

2

D.

3

解释：

We can use the rule that events are independent if their joint probability is the product of the probability of each. Pr(A) = 48%, Pr(B) = 55%, Pr(C) = 53%, Pr(A∩B) = 21% ≠ (48% * 55%), Pr(A∩C) = 25% ≠ (48% * 53%), Pr(B∩C) = 28% ≠ (55% * 53%). None of these events are pairwise independent.

P(AB)和P(A∩B)有区别么

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1 个答案

李坏_品职助教 · 2023年09月16日

嗨，努力学习的PZer你好：


P(AB)=P(A∩B)。

当A和B是独立事件的时候，P(AB)=P(A∩B)=P(A)×P（B）。


本题没有一个符合，所以都不是独立事件。

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努力的时光都是限量版，加油！

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