The game of roulette consists of a small ball and a wheel with 38 numbered pockets around the edge that includes the numbers 1 36, 0 and 00 . As the wheel is spun, the ball bounces around randomly until it settles down in one of the pockets. (a) Suppose you bet $1 on a single number and random variable X represents the (monetary) outcome (the money you win or lose). If the bet wins, the payoff is $35 and you get your money back. If you lose the bet then you lose your $1. What is the expected profit on a 1 dollar bet? (b) Suppose you bet $1 on the numbers 1 18 and random variable X represents the (monetary) outcome (the money you win or lose). If the bet wins, the payoff is $1 and you get your money back. If you lose the bet then you lose your $1. What is the expected profit on a 1 dollar bet ?