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From: eklhad@ihnet.UUCP (K. A. Dahlke)
Newsgroups: net.math
Subject: Combinatorics, Flipping a Coin With Restrictions
Message-ID: <239@ihnet.UUCP>
Date: Mon, 10-Jun-85 11:31:07 EDT
Article-I.D.: ihnet.239
Posted: Mon Jun 10 11:31:07 1985
Date-Received: Tue, 11-Jun-85 04:36:01 EDT
Distribution: net
Organization: AT&T Bell Laboratories
Lines: 16

< no two-headed coins please >
	Suppose you have a counter, initialized to 0.
Flip a fair coin N times, incrementing the counter whenever the coin
comes up heads, and decrementing the counter whenever the coin comes up tails.
As a function of N, what is the probability that the
counter never dipped below 0.
By never, I mean after each flip, the counter should be >= 0.
N	1	2	3	4	5	6	7	8
odds	1/2	2/4	3/8	6/16	10/32	20/64	35/128	70/256
	I have come up with some recursive relations that answer
the question, but I was hoping for a simpler formula.
Surely this question has been asked, and answered, before.
Happy flipping.
-- 

Karl Dahlke    ihnp4!ihnet!eklhad