A decision maker faces a problem in which the possible payoffs (in dollars) are: 1,000 3,000 6,000 9,000 10,000 12,000 Utility 0 is assigned to a payoff of $1,000 and utility 100 to a payoff of $12,000. This de- cision maker is indifferent to risk for payoffs in this range.

(a) Find the utilities for the four intermediate payoffs.

(b) For each intermediate payoff, /, find the probability p such that the decision maker is indifferent between receiving / with certainty and a wager in which $12,000 is re- ceived with probability p and $1,000 with probability (1-ph