Consider a simple game in which you will roll a six-sided die and receive $3.00 if you roll a 6. If it costs you $0.90 for each roll, what is the expected value?

Answer 1

You gain $3 if you get a 6, and always pay $0.90.

E[X] = (1/6)*3 - $0.90

Answer 2

prob of rolling a 6 = 5/36
( ways to get a 6 : [5,1 ; 4,2 ; 3,3 ; 2,4 ; 1,5 ] )

expected value = $3.00(5/36) = .41666 or 42 cents

Would you pay 90 cents for a game that has an expected value of 42 cents?