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Yuri · 2022年11月29日

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

老师我知道互斥的情况下ab等于0,但是c选项是怎么得来的呢

1 个答案

星星_品职助教 · 2022年11月30日

同学你好,

1)根据加法法则,P(A or B)=P(A)+P(B)-P(AB);

2)由于“events A and B are mutually exclusive”,所以P(AB)=0;

综上,当两个事件为互斥的时候,P(A or B)就等于P(A)+P(B)。具体公式见下图讲义截图。