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Suppose that a player with a utility function $u(x) = \sqrt{x}$ is offered the following lottery.

A fair coin is going to be flipped. If it lands on heads, the player will get $\$ 9$. If it lands on tails, he will get $\$ 6$ with a 75% probability and $\$ 9$ with a 25% probability.

Suppose he is offered another lottery: a fair coin is tossed. If it is heads, he gets zero; if tails, he gets $K$ dollars.

What is the value of $K$ that makes him indifferent between both lotteries?









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