请老师帮忙解答

问题如下：

The database of a large information organization divides the fund managers into good and medium. The data shows that the probability of a good fund manager and a medium fund manager outperforming the market is 75% and 55% respectively, assuming that the performance of the fund managers is independent of his prior year performance. And the database manager believes that only 10% of fund managers are good. Suppose a new fund manager has consistently outperformed the market for three consecutive years since he started.

2. Using the Bayesian approach，what is the approximate probability that the new manager will outperform the market next year ?

选项：

58.48%.

63.94%.

59.40%.

80.00%.

解释：

C is correct

考点：贝叶斯公式

解析：因为每个基金经理每年的业绩都是相互独立的，所以下一年的业绩与之前无关，下一年的业绩只与他是好的基金经理还是中等的有关，而第一题中我们计算出他是中等基金经理的概率是77.97%，好的基金经理的概率是1-77.97%=22.03%

所以根据贝叶斯公式

P(O) = P(O|G) x P(G) + P(O|M) x P(M)

=0.2203*75%+0.7797*55%

=16.52%+42.88%

=59.40%