You would like to invest in one of the three available investment plans: money market, bonds, or stocks. The payoffs (profits) of each plan under two possible future economic conditions, PE (poor economy) and GE (good economy), are shown below. The probability of the occurrence of PE is 0.4. PE GE Money Market 2300 3600 Bonds 3100 2600 Stocks 1500 3500 Suppose that before making the investment decision, you consider hiring an economist who can provide either U = "unfavorable" or F = "favorable" report concerning the future economic conditions. Assume that the following probability information is also available: P(UPE) = 0.7, P(FPE) = 0.3 P(UIGE) = 0.1, P(FIGE) = 0.9 What is the posterior probability P(PE|F)? a. 0.80 b. 0.18 OO OO d. 0.56