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From: stevev@tekchips.UUCP (Steve Vegdahl)
Newsgroups: net.math
Subject: Re: Probability question
Message-ID: <431@tekchips.UUCP>
Date: Tue, 17-Dec-85 14:33:05 EST
Article-I.D.: tekchips.431
Posted: Tue Dec 17 14:33:05 1985
Date-Received: Sat, 21-Dec-85 00:42:11 EST
References: <7@hplabsc.UUCP> <1478@ihlpg.UUCP>
Organization: Tektronix, Beaverton OR
Lines: 21

> > 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)?

> 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.

In particular, the probability is within 1/N! of (1 - 1/e).  For N = 52,
this means that the (1 - 1/e) approximation is accurate to 67 decimal digits.

		Steve Vegdahl
		Computer Research Lab.
		Tektronix, Inc.
		Beaverton, Oregon