Question

A decision node has two alternatives, each of which is followed by an event which has outcomes O1 and O2 with probability 0.6 and 0.4 respectively. After A1, O1 and O2 have payoffs 30 and 70. After A2, O1 and O2 have payoffs 50 and 60. What is the Expected Value at the decision node?

A) 46

B) 54

C) 50

D) 60

Answer 1

1. For Node A1:

Probability of O1 = 0.6

Payoff of O1 = 30

Expected value of O1 at Node A1 = 30*0.6 = 18

Probability of O2 = 0.4

Payoff of O2 = 70

Expected value of O2 at Node A1 = 0.4*70 = 28

Total expected value at Node A1 = 18+28 = 46

2. For Node A2:

Probability of O1 = 0.6

Payoff of O1 = 50

Expected value of O1 at Node A2 = 0.6*50 = 30

Probability of O2 = 0.4

Payoff of O2 = 60

Expected value of O2 at Node A2 = 0.4*60 = 24

Total expected value at Node A2 = 30+24 = 54

Sine the probability of occurrence of Node A1 and A2 us equal, i.e. 0.5

Hence expected value at the decision node = (0.5*46) + (0.5*54) = 50

Hence expected value at the decision node is 50.