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Probability question using Poisson...Please help?
We pick six numbers from the list of 45 numbers 1, 2, 3,...., 44, 45. We repeat this process 30 times. What is the probability that each number is picked at least once?
I know that the probability that a given number is picked is 6/45. If we model using Poisson, we get lambda=np=30(6/45)=180/45. But I am not sure where to go from here. How do I use Poisson to approximate??
1 Answer
- PaulaLv 71 decade agoFavorite Answer
P(picked at least once) = 1 - (never picked) = 1 - (39/45)^30 = 1 - 0.0137 = 0.9863
Poisson appoximation: I'll use L for lambda. L = np = 180/45 = 4.
p(k) = e^-L * L^k / k!
=> p(0) = e^-L * L^0 / 0! = e^-L = e^-4 = 0.0183
=> p(picked) = 1 - p(0) = 0.9817
So the Poisson approximation is close but not exact.