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

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

Quizplus · Accepted Answer

To find the expected value with perfect information, we simply multiply each payoff by its corresponding probability and sum the products. Doing this for each decision, we get:
- Decision 1: (0.3)(28) + (0.5)(60) + (0.2)(47) = 46.3
- Decision 2: (0.3)(120) + (0.5)(35) + (0.2)(100) = 61.5
- Decision 3: (0.3)(100) + (0.5)(25) + (0.2)(0) = 38.5
- Decision 4: (0.3)(65) + (0.5)(130) + (0.2)(80) = 95.5

Therefore, the best decision with perfect information is Decision 4, which has the highest expected payoff of 95.5.

The Following Is a Payoff Table Giving Profits for Various