Question

6 singles, 12 fives, 3 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game? State your answer in terms of dollars rounded to the nearest cent (hundredth).

Answer 1

Explanation

The fair price is the average (mean) of the dollars in the hat. It's given by the following formula:

$\operatorname{mean}=\frac{\sum ^{}_{}\text{data}}{\#\text{ of data}}.$

Applying it to our exercise, we get

$\begin{gathered} \operatorname{mean}=\frac{(1+1+\cdots+1)+(5+5+\cdots+5)+(20+20+20)+(100+100+100)}{24}=\ldots \\ \ldots\frac{6\cdot1+12\cdot5+3\cdot20+3\cdot100}{24}=\frac{426}{24}=17.75. \end{gathered}$Answer

The fair price to the play is $17.75.