For the following payoff table, the decision maker will use $P(s_1)=0\mathrm{.}20,P(s_2)=0\mathrm{.}60,$ and $P(s_3)=0\mathrm{.}20.$

$($a$)$ What alternative would be chosen according to expected value? $($Assume the decision maker wants to maximize the expected value.$)$

$d_1$

$d_2$

$($b$)$ For a lottery having a payoff of $40,000$ with probability $$ and $-15,000$ with probability $(1-p),$ the decision maker expressed the indifference probabilities shown in the following table.

Let $U(40,000)=10$ and $U(-15,000)=0$ and find the utility value for each payoff.

$($c$)$ What alternative would be chosen according to expected utility?

$d_1$

$d_2$