Final answer:
The expected value of Greg's gamble, given his utility function U(W) = W^1/2, is 3.875 utils. This calculation is based on the probabilities and utilities of the two possible outcomes, $25 and $9, which Greg could receive.
Step-by-step explanation:
Calculating the Expected Value of Greg's Gamble
To find the expected value of the gamble for Greg given his utility function U(W) = W1/2, we need to calculate the weighted average of the utilities of the outcomes, with the weights being the probabilities of these outcomes. Let's denote the wealth outcome as W, and the utility of wealth as U(W). We are given two scenarios:
- 7/16 of the time, Greg receives $25, so the utility for this outcome is U($25) = $251/2 = 5.
- 9/16 of the time, Greg receives $9, so the utility for this outcome is U($9) = $91/2 ≈ 3.
Therefore, the expected utility is calculated as:
(7/16 * 5) + (9/16 * 3)
Calculating this, we get:
(7/16 * 5) + (9/16 * 3) = (35/16) + (27/16) = (35 + 27) / 16 = 62/16 = 3.875
The expected value of Greg's gamble in terms of utility is 3.875 utils. This result cannot be directly interpreted in monetary terms because it's expressed in utilities, not dollars.