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From: gjerawlins@watdaisy.UUCP (Gregory J.E. Rawlins)
Newsgroups: net.math
Subject: Re: Combinatorics, Flipping a Coin With Restrictions
Message-ID: <7299@watdaisy.UUCP>
Date: Tue, 11-Jun-85 11:37:01 EDT
Article-I.D.: watdaisy.7299
Posted: Tue Jun 11 11:37:01 1985
Date-Received: Wed, 12-Jun-85 01:52:58 EDT
References: <239@ihnet.UUCP>
Reply-To: gjerawlins@watdaisy.UUCP (Gregory J.E. Rawlins)
Distribution: net
Organization: U of Waterloo, Ontario
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In article <239@ihnet.UUCP> eklhad@ihnet.UUCP (K. A. Dahlke) writes:
>	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.
>Surely this question has been asked, and answered, before.
>Karl Dahlke    ihnp4!ihnet!eklhad

	Yes, Feller "An Introduction to Probability Theory and its
Applications" Volume 1, section iii.2, page 75, equation 2.3. Also
see the next Theorem "Lemma 1" of section 3, pg 76, in which he
proves that this probability is the same as the probability that
it becomes 0 exactly on the n'th step (n even).
-- 
Gregory J.E. Rawlins, Department of Computer Science, U. Waterloo
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