Posted by Jordana on Sunday, February 22, 2009 at 2:20am.
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:
(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.
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