$6)$ For the payoff table below, the decision maker will use P$($s$1)=\mathrm{.}15,$ P$($s$2)=\mathrm{.}5,$ and

P$($s$3)=35$

$$

$$ s$1$ s$2$ s$3$ d

$1-5000100010,000$d$2-15,000-200040,000$ Requested: a$.$What alternative would be chosen according to expected value?

b$.$For a lottery having a payoff of $40,000$ with probability p and

$-15,000$ with probability $(1-$p$),$ the decision maker expressed the following indifference probabilities. $$ Payoff Probability $10,0000\mathrm{.}8510000\mathrm{.}60-20000\mathrm{.}53-50000\mathrm{.}50$ 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?