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Helicobacter
Jul27-10, 06:37 PM
What is the probability that at least X of K people have their birthday in August?

The answer is the obvious binomial c.d.f.:

Sum from i = X to i = K of
Choose(K,i)*(1/12)^i*(11/12)^(K-i)

What if we generalize the problem statement to any month?

What is the probability that at least X of K people have their birthday in the same month?