Birthday Problem
From: Andersen (alibandali_at_hotmail.com)
Date: 01/24/05
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Date: Mon, 24 Jan 2005 10:06:54 +0100
Hi,
I've seen the famous Birthday problem and the solution to it. But before
I saw the solution I tried to solve it myself and got a result which I
cannot numerically calculate. Please tell me if it is correct, and how
one could approximate it.
The problem is you have m people, what is the probability that two or
more of the them are born on the same day (days N=365).
My solution is:
1 - N! / ( (N-m)! * N^m )
For N=365 and m=28 for instance, this value is too huge.
The reasonning was the following, first calculate that all the m<N
people are born on different days, and take the complement of that.
Hence,
( N-0 / N )*( N-1 / N )*( N-2 / N )*...*( N-m+1 / N )
=>
PRODUCT k=0 to m-1 (N-k/N)
=>
N! / ( (N-m)! * N^m )
The first formula in this email is the complement of that.
Best regards,
Andersen
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