College Algebra, Chapter 10, 10.5, Section 10.5, Problem 10

Find the expected value (or expectation) of the games described.

A card is drawn from a deck. You win $\$104$ if the card is an ace, $\$26$ if it is a face card, and $\$13$ if it is the 8 of clubs.

The deck of 52 cards has four ace with probability $\displaystyle \frac{4}{52} = \frac{1}{3}$, twelve face card with probability
$\displaystyle \frac{12}{52} = \frac{3}{13}$ and one 8 of clubs with probability $\displaystyle \frac{1}{52}$.
So you get $\$104$ with probability $\displaystyle \frac{1}{3}, \$26$ with probability $\displaystyle \frac{3}{18}$
and $\$13$ with probability $\displaystyle \frac{1}{52}$. Thus, the expected value is

$\displaystyle 104 \left( \frac{1}{13} \right) + 26 \left( \frac{3}{13} \right) + 13 \left( \frac{1}{52} \right) = \frac{57}{4} = 14.25$

This means that if you play this game, you will make, $\$14.25$ per game.