Question

The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball.

The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball.
a. You watch a roulette wheel spin 3 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin?
b. You watch a roulette wheel spin 300 consecutive times and the ball lands on a red slot each time. What is the probability that the ball will land on a red slot on the next spin?
c. Are you equally confident of your answers to the parts (a) and (b)? Why or why not?

Answer 1

Each spin of the roulette wheel is an independent event, so the probability of landing on a red slot remains constant at approximately 47.37% for each spin, regardless of previous outcomes.

Step-by-step explanation:

The probability of landing on a red slot in roulette is independent of past spins. Therefore, the probability that the ball will land on a red slot on the next spin remains constant:

P(Red) = Number of red slots / Total number of slots = 18/38 ≈ 0.4737.

This applies to both scenarios (a) after 3 consecutive red landings and (b) after 300 consecutive red landings. The probability doesn't change because of the independent events nature of roulette spins. However, observing a streak of 300 reds would lead one to suspect a potential bias in the wheel, even though each spin is theoretically independent.