|birthday paradox, multiple matches|
Message #1 Posted by Jim Kimes on 7 July 2004, 9:03 a.m.
Hi. Everyone was very helpful with geometric progression question, circa June 15 posting. Now I need some help with interpreting an equation. You will find the one I'm talking about at: http://www25.brinkster.com/ranmath/problems/multiple.htm
It is the las equation on the page, following "which simplies to..."
which simplifies to
d! n! / (2p p!(d - n + p)! (n - 2p - 1)!)
I need this equation put into a form I can understand and therefore be able to program it into a 19BII. One thing that is confusing me is there is no 'equal to' showing. I'm presuming in the birthday paradox context that:
d = 365, n =23, p = no. of matches and then this equation solves for probability but I'm not sure.
Also, I don't understand the next sentence:
"We sum this from p = 1 to floor(n/2) for the number of ways that there may be one or more matching pairs and divide by dn for the probability. " What is he saying in layman's terms?
Plus, if you don't mind let's take an example and solve for that. Say, what is the probability of 10 matches in the U.S. Senate, consisting of 100 people. What would the probability be for this?
Thanks. You folks were immensely helpful before, as always.