The EMV of a decision with three states of nature is $33,000
If the profit/value under the states of nature A, B, and C is $10,000, $20,000, and $50,000, respectively, and states B and C have equal probabilities, determine the likelihood of state of nature A.
Let Y = the probability of state of nature B (and C)
Then the probability of state of nature A = 1 - 2Y
EMV = 10,000(1 - 2Y) + 20,000Y + 50,000Y = 33,000
70,000Y - 20,000Y = 23,000
50,000Y = 23,000
Y = .46
likelihood of state of nature A = 1 - 2(.46 ) = .08 or 8%
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