题目
John purchased 60% of the stocks in a portfolio, while Andrew purchased the other 40%. Half of John’s stock-picks are considered good, while a fourth of Andrew’s are considered to be good. If a randomly chosen stock is a good one, what is the probability John selected it?
选项
A.0.40.
B.0.30.
C.0.75.
答案
C
解析
Using the information of the stock being good, the probability is updated to a conditional probability: P(John | good) = P(good and John) / P(good). P(good and John) = P(good | John) × P(John) = 0.5 × 0.6 = 0.3. P(good and Andrew) = 0.25 × 0.40 = 0.10. P(good) = P(good and John) + P (good and Andrew) = 0.40. P(John | good) = P(good and John) / P(good) = 0.3 / 0.4 = 0.75. 使用股票将处于良好状态的信息，更新概率后，这是一个条件概率: P(John | good) = P(good and John) / P(good) P(good and John) = P(good | John)×P(John) = 0.5×0.6 = 0.3 P(good and Andrew) = 0.25×0.40 = 0.10 P(good) = P(good and John) P(good and Andrew) = 0.40 P(John | good) = P(good and John) / P(good) = 0.3 / 0.4 = 0.75