Expected Values

Question

A game is proposed in which you roll a red and blue die ( of the balanced, 6-sided variety). You get $5 if you get doubles and $3 if the red die result is greater than the blue die result. What would be the mathematically "fair" price for playing this game?

Answer 1

There are 6/36 ways to roll doubles and 15/36 ways where the red die is greater than the blue die. Since expected value is defined as E(X)=sum[x*f(x)], where X is your random variable, x is your outcome, and f(x) is your probability function, we have that E(X)=5*(6/36)+3*(15/36)=(75/36)~2.08. Therefore the "fair" price would be $2.08.