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Heart card contract

Market makingEasy

One card is drawn from a well-shuffled standard $52$ -card deck. A contract pays $10$ dollars if the card is a heart and $0$ otherwise. What is its fair value in dollars?

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Hint

How many of the cards are hearts?

Solution

The deck holds $13$ hearts, so the probability of a heart is $\frac{13}{52} = \frac{1}{4}$ .
The expected payoff is $10 \times \frac{1}{4}$ .
The fair value is $2.5$ .

Answer: $2.5$

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