Consider a lottery with three possible outcomes:
The maximum amount that a risk-neutral person would be willing to pay to play the above lottery is INR ____________.
Consider a lottery with three possible outcomes:
The maximum amount that a risk-neutral person would be willing to pay to play the above lottery is INR ____________.
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Solution and Explanation
The expected value \( E(X) \) of the lottery is given by the sum of the products of the probabilities and rewards for each outcome:
\[ E(X) = (P_1 \times R_1) + (P_2 \times R_2) + (P_3 \times R_3) \] Where:
\( P_1, P_2, P_3 \) are the probabilities of outcomes I, II, and III, respectively.
\( R_1, R_2, R_3 \) are the rewards corresponding to outcomes I, II, and III, respectively.
Substitute the given values:
\[ E(X) = (0.2 \times 25) + (0.3 \times 50) + (0.5 \times 100) \] \[ E(X) = 5 + 15 + 50 = 70 \]
Thus, the maximum amount a risk-neutral person would be willing to pay to play the lottery is INR 70.
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