Question

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.

Decision Alternative	States of Nature
	s1	s2	s3
d1	240	90	15
d2	90	90	65

Suppose that the decision maker obtained the probabilities

P(s₁) = 0.65, P(s₂) = 0.15,

and

P(s₃) = 0.20.

Use the expected value approach to determine the optimal decision.

EV(d₁) = EV(d₂) = The optimal decision is  ? d₁ d₂

Answer 1

Decision alternative	s1	s2	s3
d1	240	90	15
d2	90	90	65

P(s1)=	0.65
P(s2)=	0.15
P(s3)=	0.2

expected value for decision 1 (d1)=               240*0.65+90*0.15+15*0.2=           172.5
                          
expected value for decision 2 (d2) =                90*0.65+90*0.15+65*0.2=           85
since,    E(d1)>E(d2), recommeded decision is d1                     
its expected value=   172.5