Respuesta :
The fair price to play the game is $23.61
Explanation:Number of singles = 5
number of fives = 8
Number of twenties = 4
number of $300 = 1
Total number = 5 + 8 + 4 + 1 = 18
fraction for each:
5/18 chance of getting singles
8/18 chance of getting fives
4/18 chance of getting twenties
1/18 chance of getting $300
We find the Expected values:
[tex]\begin{gathered} \text{singles = 1} \\ \text{Expected }value\text{ = (}\frac{5}{18}\text{ }\times1)\text{ +(}\frac{\text{ 8}}{18}\times\text{ 5)+ (}\frac{\text{4}}{18}\times20)\text{ + (}\frac{\text{1}}{18}\times300) \\ \text{Expected }value\text{ =}\frac{1}{18}\text{ \lbrack(}5\text{ }\times1)\text{ +(}8\times\text{ 5)+ (}4\times20)\text{ + (}1\times300)\rbrack \\ \text{Expected value =}\frac{1}{18}\text{(}5\text{ + 40 + 80 + 300)}_{} \\ \\ \text{fair price = }\frac{Total\text{ money in the hat}}{total\text{ number of bills}} \\ \text{fair price = }\frac{1}{18}\text{(}5\text{ + 40 + 80 + 300)}_{} \end{gathered}[/tex][tex]\begin{gathered} \text{fair price = }\frac{1}{18}\text{(}425\text{)}_{} \\ \text{fair price = \$23.61} \end{gathered}[/tex]In the absence of further information, fair price is $23.61
