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Fair price for $3$ heads

Expected valueEasy

A game flips $3$ fair coins and pays $20$ dollars if all of them show heads and nothing otherwise. What entry fee, in dollars, makes the game fair (expected net result $0$ )?

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Hint

A fair fee equals the expected payout.

Solution

All $3$ coins show heads with probability $\frac{1}{8}$ .
The expected payout is $20 \times \frac{1}{8}$ .
A fair fee equals that payout, so it is $\frac{5}{2}$ .

Answer: $\frac{5}{2}$

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