Please perform computerized solution, not handwritten. Thanks A manager must cho

Question

Please perform computerized solution, not handwritten. Thanks

A manager must choose between two courses of action (A or B). He is thinking about having a market survey performed at a cost of $5,000. If the market survey is conducted, the outcome will either be favorable (Fav) or unfavorable (Unf). Ultimately, the out- come will either be a business success (S) or a business failure (F). For option A, success $50,000 profit, failure = $5,000 loss. For option B, success = $30,000 profit, failure = $10,000 profit. The market survey, if performed, would cost $5,000. The appropriate probabilities are Pr(F) = 6, Pr(Favis) = 9, and Pr(Unf F-8. Determine the appropriate posterior probabilities [Pr(S/Fav), Pr(F|Fav), Pr(S|Unf), and Pr(F|Unf)] and perform a backward induction analysis to determine if the experimental information should be obtained.

Explanation / Answer

A manager must choose between two course of action A or B.

For option A,

Success = $50000 profit, Failure = $5000 loss.

For Option B,

Success = $30000 profit, Failure = $10000 loss.

S - Success , F - failure, Fav - favorable, Unf - unfavorable

P(F) = 0.6, P(Fav/S) = 0.9, P(Unf/F) = 0.8, P(S) =1 -P(F) = 1 - 0.6 = 0.4,P(Fav/F) = 1 - P(Fav/S) = 1 - 0.9 = 0.1

We have to find posterior probabilities but they donot ask to find probability separately for option A or option B theirefore we find these probabilities from given probabilities only.

P(S/ Fav) = P(Fav/S) * P(S) / (P(Fav/S) * P(S) + P(Unf/F) * P(F))

= (0.9 * 0.4) / (0.9 *0.4 + 0.8 *0.6)

= 0.36 / (0.36 +0.48)

P(S/ Fav) = 0.4286

P(F/ Fav) = P(Fav/F) * P(F) / (P(Fav/F) * P(F) + P(Unf/F) * P(F))

= 0.1*0.6 / (0.8 *0.6+ 0.1 * 0.6)

P(F/ Fav) = 0.1111

P(S/Unf) = P(Fav/S) *P(S)/ ((P(Fav/S)) + P(Unf/F))

= 0.9 *0.4 /(0.9 + 0.8)

P(S/Unf)  = 0.5294

P(F/Unf) = P(Unf/F)*P(F) / (P(Unf/F)*P(F) + P(Fav/S)*P(S))

= 0.48 / (0.48 + 0.36)

P(F/Unf) = 0.5714

Backword induction analysis determines same probabilities.

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