Georgeis forecasting a stock's performance. He based his forecast on the state of the economy and divides the economy's performance into three categories of "GOOD", "NEUTRAL" and "POOR". He also divides the stock's performance into three categories of "increase", "constant" and "decrease". In his estimation:
* 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%.
Mary, his supervisor, asks him to estimate the probability that the state of the economy is neutral given that the stock performance is constant. George's best assessment of that probability is closest to:
A.  15.5%
B.  19.6%
C.  20.0%
D.  38.7%
Answer:D
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) = 0.387