If you pay $3.50 to play the game in Problem 62 (the dice are rolled once) and you are returned the dollar amount corresponding to the sum on the faces, what is the expected value of the game? Is the game fair? If it is not fair, how much should you pay in order to make the game fair?

Problem 62

Two fair (not weighted) dice are each numbered with a 3 on one side, a 2 on two sides, and a 1 on three sides. The dice are rolled, and the numbers on the two up faces are added. If X is the random variable associated with the sample space

S = {2, 3, 4, 5, 6}: