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From: brengle@hplabsc.UUCP (Tim Brengle)
Newsgroups: net.math
Subject: Probability question
Message-ID: <7@hplabsc.UUCP>
Date: Wed, 11-Dec-85 20:58:36 EST
Article-I.D.: hplabsc.7
Posted: Wed Dec 11 20:58:36 1985
Date-Received: Mon, 16-Dec-85 22:35:39 EST
Organization: Hewlett Packard Labs, Palo Alto CA
Lines: 20

Upon finding out that I claimed to have been a mathematician once upon a
time, a co-worker asked me a probability question.  Now, I never did all
that well in probability or combinatorics, so I am passing this on in
hopes that someone out there might be able to answer it or give me an
appropriate pointer:

You have two decks of normal playing cards, say red-backed and blue-backed.
You shuffle each individually, and place them on the table.  Turn the top
card of each deck face up and place it on the table.  Repeat the turning
process until all cards have been turned face up.

What is the probability that at least one pair of cards turned at the same
time are exactly the same (except for the color of their backs)?

I think that the problem is equivalent to having a single deck of cards
numbered from 1 to 52 and determining the probability that at least one
card occurs at its numbered position.

			Thanks in advance,
				Tim Brengle