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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?

Sagot :

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:

[tex]\begin{gathered} \text{fair price}=1\times\frac{8}{23}+5\times\frac{10}{23}+20\times\frac{2}{23}+100\times\frac{3}{23} \\ =\frac{8}{23}+\frac{50}{23}+\frac{40}{23}+\frac{300}{23} \\ =\frac{8+50+40+300}{23} \\ =\frac{398}{23} \\ =17.30 \end{gathered}[/tex]

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

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