How many times will the ball land on red or black?

Question

A roulette wheel has 38 slots around the rim. The first 36 slots are numbers from 1 to 36. Half of the 36 slots are red, the other half are black. The remaining 2 slots are numbered 0 and 00 and are green. If the roulette wheel is spun 114 times, predict about how many times the ball will land on red or black?

Answer 1

The quantity that Mark mentions (i.e. (36/38)¹¹⁴) is the probability that you get red or black on all 114 independent spins. But that's hardly a prediction for the number of times the ball will land on red or black.

 

The probability of getting red or black on a single spin is 36/38. One way to interpret this probability is by saying something like, "If I spun the wheel 38 times, about 36 of those spins would come up red or black." Of course, we can't say ahead of time that it'll be exactly 36 times: this is a random process, subject to chance variation. But on average, we expect to see about 36 successes (red or black) in 38 trials (spins).

 

Of course, the question didn't ask about 38 trials - it asked about 114 trials. And if we expect to see 36 successes in 38 trials, then we should also expect to see 3*36=108 successes in 3*38=114 trials.

 

(To better understand the distribution of the number of reds/blacks in 114 spins, you could model this as a Binomial(n=114, p=36/38) random variable. But that might be outside the scope of your level of probability.)

Answer 2

Each time the ball is rolled it has a 36/38 probability of landing on red or black.

For 114 spins, the probability is (36/38)¹¹⁴.