Calculating Probability of 3 Pennies in 30 Boxes Using Poisson Distribution

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SUMMARY

The probability of exactly 3 pennies in box number 1 from a total of 100 pennies distributed across 30 boxes can be calculated using the binomial distribution rather than the Poisson distribution. The correct parameters for the binomial distribution are N = 100 (total pennies), k = 3 (pennies in box 1), and p = 1/30 (probability of a penny landing in box 1). The initial calculation using the Poisson distribution yielded 0.22021, while the correct binomial calculation results in a probability of 0.22345.

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little neutrino
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One hundred pennies are being distributed independently and at random into 30 boxes, labeled 1, 2, ..., 30. What is the probability that there are exactly 3 pennies in box number 1?

I tried using a Poisson distribution f(x) = (e^-λ)*(λ^x)/x! , with λ = 100/30 = 10/3 and x = 3. I got 0.22021 (5 s.f.), but the answer key is 0.22345. Am I using the wrong distribution? Thanks!
 
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For anyone penny, what is the probability that it will end up in box # 1?
Use a binomial distribution...N = number of pennies. k = 3. p = probability of landing in box #1.
 
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RUber said:
For anyone penny, what is the probability that it will end up in box # 1?
Use a binomial distribution...N = number of pennies. k = 3. p = probability of landing in box #1.

Ok I got it! Thanks! :)
 

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