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Break-even prize

Expected valueEasy

A risk-neutral gambler is exactly indifferent between a sure $15$ dollars and a ticket that pays a prize of $P$ dollars with probability $\frac{1}{4}$ and nothing otherwise. What is $P$ ?

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Hint

Risk-neutral means comparing expected values.

Solution

The ticket has expected value $\frac{P}{4}$ .
Indifference requires $\frac{P}{4} = 15$ .
So $P = 60$ .

Answer: $60$

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