In its simplest form, betting $1 upon a color in the game of roulette provides a 18/38 probability of winning $1 and a 20/38 probability of losing $1.
(a) Use the CLT to approximate the probability that your net winnings will be negative if you play 50 times.
(b) Use the CLT to approximate the probability that your net winnings will be negative if you play 500 times.
(c) How does these probabilities compare? Explain why this makes sense.