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罗密欧C · 2020年01月13日

问一道题:NO.PZ2020010301000008

问题如下:

There are two companies in an economy, Company A and Company B. The default rate for Company A is 10%, and the default rate for Company B is 20%. Assume defaults for the two companies occur independently.

What is the probability that either Company A or Company B defaults?

选项:

A.

2%

B.

28%

C.

8%

D.

30%

解释:

Pr(AB) = Pr(A) + Pr(B) - Pr(AB) = 10% + 20% - 2% = 28%.

Pr(A∪B) = Pr(A) + Pr(B) - Pr(A∩B) = 10% + 20% - 2% = 28%.


请问一下为什么要减去2%?

1 个答案

orange品职答疑助手 · 2020年01月14日

同学你好,P(A+B) = P(A)+P(B)-P(AB),而因为事件A和事件B独立,因此P(AB)=P(A)*P(B),这减去的2%就是P(AB)