An American roulette wheel has 38 pockets: 18 red, 18 black, and 2 green (these are 0 and 00). The simplest bet in roulette is to bet on red: if the ball falls in a red pocket on the next spin, the gambler wins back double what they bet (i.e. if they bet $1 on red and win, they will now have $2). Consider these two bets: I. Bet $3 on red for one spin II. Bet $1 on red for three spins Let W1 be the amount of money you would win making the first bet, and let W2 be the amount of money you would win from the second. Follow these steps to compare these two bets:

(a) Compute E[W1] and E[W2]

(b) Compute Var(W1) and Var(W2)

(c) Compute P(W1 > 0) and P(W2 > 0)

(d) Which of these two bets would you prefer to make? Explain.