Question

Suppose you pay $0.90 to roll a fair 12-sided die with the understanding that you will get $2.10 back for rolling a 1, 2, 3, 4, or 5. Otherwise, you get no money back. What is your expected value of gain or loss?

Answer 1

-$0.025

Explanation:

p(win) = 5/12

p(loss) = 7/12

expected value of a win: (2.10 - 0.90)(5/12)

expected value of a loss: (-0.90)(7/12)

overall expected value:

(2.10 - 0.90)(5/12) + (-0.90)(7/12) =

= 1.2 × 5/12 - 0.9 × 7/12

= -0.025