The following is a payoff table giving profits for various situations. The probabilities for states of nature A,B,and C are 0.3,0.5,and 0.2,respectively.If a perfect forecast of the future were available,what is the expected value with this perfect information?
A)130
B)160
C)166
D)36
E)None of the above

Question

The following is a payoff table giving profits for various situations.  The probabilities for states of nature A,B,and C are 0.3,0.5,and 0.2,respectively.If a perfect forecast of the future were available,what is the expected value with this perfect information?
A)130 
B)160 
C)166 
D)36 
E)None of the above

Quizplus · Accepted Answer

To find the expected value with perfect information, we need to multiply each payoff by its corresponding probability and then sum them up. 
Expected value with perfect information = (0.3)(110) + (0.3)(130) + (0.5)(120) + (0.5)(160) + (0.2)(100) + (0.2)(70) 
= 33 + 39 + 60 + 80 + 20 + 14 
= 246

The best choice would be the one that gives the highest expected value, which is Option B with an expected value of 160.

The Following Is a Payoff Table Giving Profits for Various