Question

suppose a standard six sided die is ed and you receive $4.50 for every dot showing on the top of the die. What should the cost of playing the game be in order to make it a fair game?

Answer 1

Answer:

$15.75

Explanation:

The game is fair if the expected value is equal to the cost of playing the game. To calculate the expected value, we need to identuty how much do you win for each option of the die, so:

one dot: $4.50

two dots: 2 x $4.50 = $9

three dots: 3 x $4.50 = $13.5

four dots: 4 x $4.50 = $18

five dots: 5 x $4.50 = $22.5

six dots: 6 x $4.50 = $27

Since each side of the die has an equal probability, we can calculate the expected value as the mean of the quantities above, so:

$\begin{gathered} E=\frac{4.5+9+13.5+18+22.5+27}{6} \\ E=15.75 \end{gathered}$

Therefore, the game is fair is the cost is $15.75