Question

8 singles, 10 fives, 2 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?

Answer 1

The total number of bills are 23.

The probability to get single = 8/23

The probability to get five = 10/23

The probability to get twenty = 2/23

The probability to get a hundred = 3/23

So, the fair price to play this game is calculated below:

`\begin{gathered} \text{fair price}=1*(8)/(23)+5*(10)/(23)+20*(2)/(23)+100*(3)/(23) \\ =(8)/(23)+(50)/(23)+(40)/(23)+(300)/(23) \\ =(8+50+40+300)/(23) \\ =(398)/(23) \\ =17.30 \end{gathered}`

Thus, the fair price to play this game is $17.30