Question

6 singles, 7 fives, 3 twenties, and 2 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?

Answer 1

Fair price to play this game is $16.72

Step-by-step explanation:
`\begin{gathered} \text{Given:} \\ 6\text{ singles, 7 fives, 3 twenties and 2 hundred dollar bills in a hat} \\ \end{gathered}`

To find the fair price, we divide the total amount by the number of bill denominations given

`\text{fair price = }\frac{total\text{ amount in the hat}}{nu\text{mber of bills in the hat}}`
`\begin{gathered} nu\text{mber of bills = }6\text{ + 7 + 3 + 2 = 18} \\ \\ \text{singles = 1} \\ 6\text{ singles = 6 }*\text{ 1} \\ 7\text{ fives = 7}*\text{ 5} \\ 3\text{ twenties = 3}*20 \\ 2\text{ hundred = 2 }*\text{ 100} \\ \\ \text{Total amount in the hat = 6 }*\text{ 1 + 7}*\text{ 5 + 3}*20\text{ + 2 }*\text{ 100} \\ \text{Total amount = 6 + 35 + 60 + 200 = 301} \end{gathered}`
`\begin{gathered} \text{fair price = }(301)/(18) \\ \text{fair price = 16.72} \end{gathered}`

Fair price to play this game is $16.72