You are evaluating investment alternatives for a ski resort.There are four alternative investments and their payoffs (in $10,000s)are shown in the following table, depending on the snow conditions for the next season. $\begin{array}{r} \text { Snow Conditions }\ \begin{array}{ccc} \text { Investment } & \text { Good } & \text { Bad } \ d_{1} & 3 & 1 \ d_{2} & 8 & 0 \ d_{3} & 12 & -4 \ d_{4} & 18 & -12 \end{array}\end{array}$ If you use the EMV criterion and you decide investment d₂, then the probability that the snow conditions are good is ______. A)more than 0.5 B)more than 0.17 C)more than 0.25 and less than 0.67 D)less than 0.17 or more than 0.5 E)more than 0.17 and less than 0.5

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The Expected Monetary Value (EMV) for each investment is calculated as EMV = p(Good) * Payoff(Good) + p(Bad) * Payoff(Bad), where p(Good) + p(Bad) = 1. To find the probability where d1 is preferred over d2, d3, and d4, we set up inequalities based on their EMVs and solve for p(Good). For d1 to be preferred, its EMV must be higher than that of the others under the same probability distribution of snow conditions. By comparing d1 with each of the other investments and solving the resulting inequalities for p(Good), we find the range of probabilities where d1 has the highest EMV. This approach leads to the conclusion that the probability of good snow conditions must be more than 0.17 and less than 0.5 for d1 to be the preferred investment based on the EMV criterion.

You Are Evaluating Investment Alternatives for a Ski Resort If You Use the EMV Criterion and You Decide Investment