Roulette. An American roulette wheel consists of 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on each of the 38 numbers. A gambler is playing roulette and bets $10 on red each time. If the ball lands on a red number, the gambler wins $10; otherwise, the gambler loses $10. What is the probability that the gambler will be ahead after

a. 100 bets?

b. 1000 bets?

c. 5000 bets?

(Hint: The gambler will be ahead after a series of bets if and only if he or she has won more than half the bets.)