Re: Birthday Problem

From: Paul Nutteing (nutteing_at_quickfindit.com)
Date: 01/25/05 

Date: Tue, 25 Jan 2005 07:36:35 -0000

"Andersen" <alibandali@hotmail.com> wrote in message
news:35m801F4ntauiU1@individual.net...
> 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
>
> ps. I originally posted this on sci.stat.math and sci.stat.edu but got
> no response. Maybe people here are better at approximating expressions
> etc. ds.

This is a useful analysis of the Birthday problem
http://images.beggerlybend.com/puzzles/birthdays.html
There was a minor typo that he corrected.
Forensic 'scientists' to-a-man have a problem
over-calculating the probability of false matches
with DNA profiles in similar manner to the Birthday problem

What they aren't telling you about DNA profiles
and what Special Branch don't want you to know.
http://www.nutteing2.freeservers.com/dnapr.htm
or nutteingd in a search engine

Valid email nutteing@fastmail.....fm (remove 4 of the 5 dots)
Ignore any other apparent em address used to post this message -
it is defunct due to spam.