A box contains one each of $1, $5, $10, $50, and $100 bills. You reach in and withdraw one bill. What is the expected value to the nearest cent?

Question

Quizplus · Accepted Answer

The expected value is the sum of each possible outcome multiplied by its probability. The total value of the bills is $166.50, and there are five bills, so the average value of one bill is $33.30. However, since each bill has an equal chance of being selected, the probability of picking any one bill is $\frac{1}{5}$. Therefore, the expected value is $\frac{1}{5}(\$1)+\frac{1}{5}(\$5)+\frac{1}{5}(\$10)+\frac{1}{5}(\$50)+\frac{1}{5}(\$100)=\$33.20$.

A Box Contains One Each of $1, $5, $10, $50