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From: kpv@ulysses.UUCP (Phong Vo)
Newsgroups: net.math
Subject: Ballot counting problem (variation)
Message-ID: <835@ulysses.UUCP>
Date: Fri, 27-Apr-84 14:23:34 EST
Article-I.D.: ulysses.835
Posted: Fri Apr 27 14:23:34 1984
Date-Received: Sat, 28-Apr-84 09:38:21 EST
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 17

William Tanenbaum has given a solution to the problem:
	In a two candidate election, the winner gets p votes
	and the loser gets q votes (p > q). The ballots are
	randomly shuffled and counted one at a time.
	What is the probability that the winner will always
		BE AHEAD
	at any point during the counting?

Now the variation:
	What is the probability that the winner will always
		DO AT LEAST AS WELL AS THE LOSER
	at any point during the counting?

That is, at any time t during the counting, if w(t) is the number of votes
that the winner receives and l(t) is the number of votes that the loser
receives, then w(t) >= l(t).
In the original problem, it is required that w(t) > l(t).