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From: tan@ihlpg.UUCP (Bill Tanenbaum)
Newsgroups: net.math
Subject: Re: Probability question
Message-ID: <1478@ihlpg.UUCP>
Date: Sat, 14-Dec-85 00:26:17 EST
Article-I.D.: ihlpg.1478
Posted: Sat Dec 14 00:26:17 1985
Date-Received: Sat, 14-Dec-85 23:40:00 EST
References: <7@hplabsc.UUCP>
Organization: AT&T Bell Laboratories
Lines: 28

> 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
------------
The probability is extremely close to 1 - 1/e, or about 63%.  The
probability that one or more cards will be in their proper 
position in an N card deck is greater than (1 - 1/e) for odd N,
and less than (1 - 1/e) for even N.  In either case, the probability
approaches the limit of (1 - 1/e) as N increases.
-- 
Bill Tanenbaum - AT&T Bell Labs - Naperville IL  ihnp4!ihlpg!tan