题目
John is forecasting a stock's performance in 2010 conditional on the state of the economy of the country in which the firm is based. He divides the economy's performance into three categories of "GOOD", "NEUTRAL" and "POOR" and the stock's performance into three categories of "increase", "constant" and "decrease".He estimates: ? The probability that the state of the economy is GOOD is 20%. If the state of the economy is GOOD, the probability that the stock price increases is 80% and the probability that the stock price decreases is 10%. ? The probability that the state of the economy is NEUTRAL is 30%. If the state of the economy is NEUTRAL, the probability that the stock price increases is 50% and the probability that the stock price decreases is 30%. ? If the state of the economy is POOR, the probability that the stock price increases is 15% and the probability that the stock price decreases is 70%.Billy, his supervisor, asks him to estimate the probability that the state of the economy is NEUTRAL given that the stock performance is constant.John's best assessment of that probability is closest to:
选项
A.15.5%
B.19.6%
C.20.0%
D.38.7%
答案
D
解析
Use Bayes' Theorem:P(Neutral | Constant) = P(Constant | Neutral) × P(Neutral) / P(Constant)= 0.2 × 0 3/(0.1 × 0.2 + 0.2 × 0.3 + 0.15 × 0.5) = 0.387A This is the Prob (Constant)B This is the Prob (Constant)C This is the Prob (Neutral | Decrease)使用贝叶斯公式：P(Neutral | Constant) = P(Constant | Neutral) × P(Neutral) / P(Constant)= 0.2 × 0 3/(0.1 × 0.2 0.2 × 0.3 0.15 × 0.5) = 0.387A是Prob (Constant)B是Prob (Constant)C是Prob (Neutral | Decrease)