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# Comparing Lotteries

MICRO-@SYBIB

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? A 0 B$42.25

C

$10.5625 D$12.00