College Algebra, Chapter 10, 10.5, Section 10.5, Problem 18

A slot machine has three wheels, and each wheel has 11 positions: the digits $0,1,2...9$ and the picture of a watermelon. When a quarter is placed in the machine and the handle is pulled, the three wheels spin independently and come to rest. When three watermelons show, the payout is $\$ 5$; otherwise, nothing is paid. What is the expected value of this game?

The probability of showing the watermelon in three wheels is $\displaystyle \frac{1}{11} \times \frac{1}{11} \times \frac{1}{11} = \frac{1}{1331}$. Thus, the expected value is

$\displaystyle 5 \left( \frac{1}{1331} \right) - 0.25 \left( \frac{1330}{1331} \right) = -0.25$

This means that if you play this game, you will lose, on average, 25 cents per game.