you are playing a simple game with one fair die If you roll

you are playing a simple game with one fair die . If you roll a 6 , you win 10 dollars . if you roll a 1,2,3,4,or 5 , you lose 2 dollars .what is your expected payout ?

Solution

a fair die the probability for each number is 1/6

x * P((x)

1/6 * 10 + 1/6 * -2 + 1/6 * -2 + 1/6 * -2 + 1/6 * -2 + 1/6 * -2

1.67 + -0.333 - 0.333 - 0.333 - 0.333 -0.333

Expected payout = 0