statistics help needed
posted by Jordana .
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.
B. The ball does not fall into any green slots.
C. The ball falls into black slots 11 or more times.
D. The ball falls into red slots 12 or fewer times.
We will be glad to critique your thinking.
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.
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:
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.