Question

An executive has to make a decision regarding 3 alternatives: DI, D2, and D3. The outcome based on the 3 alternatives are: R1 with probability 0.5, R2 with robability 0.3 and R3 with probability 0.2.The returns matrix between various decision alternatives and their outcomes are given below: Q4. R R2 R3 DI 14 9 10 D2 9 10 10 D3 8 10 11 Prepare the decision situation in the form of a decision tree and select the best preferred decision

Answer 1

The decision tree is following:

R1 0.5 14 R2 0.3 R3 0.2 11.7 D1 2 10 R1 0.5 R2 0.3 R3 0.2 9.5 Max EV = 11.7 D2 Decision: D1 10 10 R1 0.5 R2 0.3 R30.2 9.2 10 4

Expected Value (EV) of D1 = .5*14+.3*9+.2*10 = 11.7

Expected Value (EV) of D2 = .5*9+.3*10+.2*10 = 9.5

Expected Value (EV) of D3 = .5*8+.3*10+.2*11 = 9.2

Maximum EV is 11.7 pertaining to decision D1. therefore, D1 is the preferred decsion.