Question

Fair Games. Using the combinations of 2 dice you just created

If you roll a sum of 5, you will win $2. If you roll a sum of 10, you will win $5.
1) Calculate the probability of rolling a sum of 5.
reduced fraction:___
2) calculate the probability of rolling a sum of 10
reduced fraction:___
3) What is the expected payout of the game? $___
4) How much should be charged to play this game to make it fair? $___
Hint: Expected profit = cost of playing - expected payout
5) If the charge is $4 per game, how much will the house profit off 100 plays? $___

Answer 1

1) P(sum of 5) = 4/36 = 1/9

2) P(sum of 10) = 3/36 = 1/12

3) E = (1/9)($2) + (1/12)($5) = 13/18 = $.72

4) $.72 should be charged to make this game fair.

5) 100($4 - $.72) = 100($3.28) = $328