CMA Intermediate · Management Accounting · Decision Theory
Two acts are compared in two states. Act A pays ₹100 thousand in S1 and ₹20 thousand in S2. Act B pays ₹50 thousand in S1 and ₹70 thousand in S2. At what probability of S1 would the EMVs of A and B be equal?
The EMVs are equal at a probability of 0.5 for S1. Act A's EMV is 20 + 80p and Act B's is 70 − 20p; equating them gives 100p = 50. At p = 0.5 both acts have an EMV of ₹60 thousand.
- A0.40
- B0.50Correct
- C0.60
- D0.625
Explanation
Let p be the probability of S1. EMV of A = 100p + 20(1−p) = 20 + 80p. EMV of B = 50p + 70(1−p) = 70 − 20p. Setting equal: 100p = 50, so p = 0.5. Check: A = 60 and B = 60. The value 0.625 comes from wrongly dividing 50 by 80.
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