In the dice game known as "seven," two fair dice are rolled and the sum of scores is counted. You bet on "manque" (that a sum of 2, 3, 4, 5 or 6 will result) or on "passe" (that a sum of 8, 9, 10, 11 or 12 will result). The sum of 7 is a fixed winner for the house. A winner receives a payoff that is double the amount staked on the game. Non winners forfeit the amount staked. Define an appropriate probability space for this experiment. Then calculate the expected value of the payoff per dollar staked.