问题如下:
After estimating the probability that an investment manager will exceed his benchmark return in each of the next two quarters, an analyst wants to forecast the probability that the investment manager will exceed his benchmark return over the two-quarter period in total. Assuming that each quarter’s performance is independent of the other, which probability rule should the analyst select?
选项:
A. Addition rule
B. Multiplication rule
C. Total probability rule
解释:
B is correct.
Because the events are independent, the multiplication rule is most appropriate for forecasting their joint probability. The multiplication rule for independent events states that the joint probability of both A and B occurring is P(AB) = P(A)P(B).
两个均超过应该是“both”, 而这里说“in total”可以理解为一个月没超过而另一个月超过了很多时,也可以达到两个月总共“in total”超过了。所以应该用全概率rules,不是吗?