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Prime roll payoff

Market makingEasy

A contract pays $20$ dollars if one roll of a fair $6$ -sided die shows a prime number and $5$ dollars otherwise. What is its fair value in dollars?

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Hint

Count the prime faces first.

Solution

The prime faces are $2$ , $3$ and $5$ , so the probability of a prime is $\frac{1}{2}$ .
The expected payoff is $20 \times \frac{1}{2} + 5 \times \frac{1}{2}$ .
The fair value is $12.5$ .

Answer: $12.5$