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Path: utzoo!linus!decvax!harpo!seismo!rlgvax!cvl!elsie!mark
From: mark@elsie.UUCP
Newsgroups: net.math
Subject: A problem in probability : ref needed.
Message-ID: <153@elsie.UUCP>
Date: Tue, 6-Dec-83 13:34:10 EST
Article-I.D.: elsie.153
Posted: Tue Dec  6 13:34:10 1983
Date-Received: Fri, 9-Dec-83 02:23:45 EST
Organization: NIH-LCM, Bethesda, MD
Lines: 26

I need a reference to what should be a rather common problem in statistics.
What is the probability of finding m events in N tries where the probability
of an event is given by p(i), where 0 <= i <= m <= N, and p(i) <= p(i+1).
That is, the probability of an event is a function of the number of previous
successes, and , in general, that probability decreases with each success.

For example: if we have a number of balls, B of which r are red and b are
blue (r+b = B), what is the probability of picking out m red balls (m <= r)
in N tries where each RED ball is discarded after it is picked and the BLUE
balls are returned to the pile.

I recognize that the binomial distribution is applicable in the case where
the probability of an event remains constant, but in this case, the
probability decreases. I've worked out an approximate solution, based on the
binomial distribution, that is close enough for the program I've written.
But I haven't been able to find a reference to this problem in any of the
standard references I'm capable of understanding (Knuth; Snedecor & Cochran;
etc.). I need to reference this stuff in a biologically oriented paper 
(I'm a biochemist by training), and I don't want to try to include
the proof in same (Dear Dr. Miller, We don't feel this paper is appropriate
for our journal, try the ACM.). Also, I don't want to reproduce something
that was probably done by some German in the late 18th century. Feel free to
reply either directly or over net.math. Thanx in advance.
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