Question

The following profit payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Suppose that the decision maker obtained the probability assessments P(S₁) = 0.65, P(S₂) = 0.20, and P(S₃) = 0.15.

	State of Nature
Decision Alternative	S1	S2	S3
d1	150	175	50
d2	175	75	100

Use the expected value approach to determine the optimal decision.

The optimal decision is?

Answer 1

Decision probability assessment : P (S1)=0.65, P(S2)=0.20, P(S3)=0.15

Expected value approach:

Decision 1 = (150 × 0.65) + (175×0.20) + (50×0.15)

= 97.50 + 35 + 7.5 = 140 Profit

Decision 2 = (175×0.65) + (75×0.20) + (100×0.15)

= 113.75 + 15 + 15 = 143.75 Profit

Optimal Decision : Decision 2

Because Decision 2 generating more profit payoff than Decision 1.