Question

In the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 24 times, find the probability of the following events.

A. The ball falls into the green slots 4 or more times.

Probability =

B. The ball does not fall into any green slots.

Probability =

C. The ball falls into black slots 11 or more times.

Probability =

D. The ball falls into red slots 12 or fewer times.

Probability =

Answer 1

We will be glad to critique your thinking.

Answer 2

I don't know if I use the poisson function in excel. I just don't know how to start the problem.
I can find the probability of hitting a green slot in one time but not multiple times.

Answer 3

Poisson statistics is not the only way to do these problems, but it can provide an approximate result for some.

For B, the probability is that of no-green 24 times in a row. (36/38)^24 = (18/19)^24 = 0.273 That was easy

For A, add the probabilities of getting green 4,5,6...24 etc times in 24 attempts. The sum will rapidly converge.
Probability of 4 green:
(1/19)^4*(18/19)^20*C(24,4)= 0.02765
Probability of 5:
(1/19)^5*(18/19)^19*C(24,5) = 0.00614
Probability of 6:
(1/19)^6*(18/19)^18*C(24,6) = 0.00108
Probability of 7:
(1/19)^7*(18/19)^17*C(24,7) = 0.00015
Probability of 4 or more: 0.0350

If a Poisson distribution is used, for n = 24 spins with p = 1/19 probability of green each time, a = np = 1.26316
P(4) = a^4*e^-1.236/4! = 0.03082
You still have to add up P(5), P(6) etc.