Question

Suppose it costs $36 to roll a pair of dice. You get paid 5 dollars times the sum of the numbers that appear on the dice. What is the expected payoff of the game? Is it a fair game?

Answer 1

-1.833, not a fair game

Explanation:

Given that it costs $36 to roll a pair of dice. You get paid 5 dollars times the sum of the numbers that appear on the dice

We have sample space for sum of numbers of dice as

sum 2 3 4 5 6 7 8 9 10 11 12

Prob 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36

X gain 10 15 20 25 30 35 40 45 50 55 60

Prob 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36

Expected payoff =
`(10+30+60+100+150+180+200+180+150+110+60)/(36) \\=34.167`

Cost of playing the game = 36

Net pay off by playing (expected) =
`34.167-36\\=-1.833`

Since expected pay off is negative it is not a fair game.