1. Roulette is a relatively slow casino game. Typically, the dealer spins the roulette wheel 40 to 50 times per hour. On a roulette wheel there are 18 red slots and 18 black slots numbered 1 to 36 and two green slots numbered 0 and 00. If I bet a $1 on red and the ball comes to rest in a red slot, then I win a dollar and the house loses a dollar. If not, I lose a dollar and the house wins a dollar. Suppose that the ball has an equal probability of coming to rest in any slot and that each spin is independent. The probability of landing in a red slot is 18/38. I intend to place a sequence of $1 bets on red (at a charity event, of course).

A. What is the mean of my return (change in wealth) from a single bet?

B. What is the variance of my return from a single bet?

C. What is the probability that after 121 bets I will have at least as much money as I started with?