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From: doyle@apple.UUCP (Ken Doyle)
Newsgroups: net.math
Subject: Re: probability formula
Message-ID: <42427@apple.UUCP>
Date: Wed, 2-Oct-85 17:00:15 EDT
Article-I.D.: apple.42427
Posted: Wed Oct  2 17:00:15 1985
Date-Received: Sat, 5-Oct-85 07:08:13 EDT
References: <2249@utcsstat.UUCP>
Reply-To: doyle@apple.UUCP (Ken Doyle)
Organization: Advanced Development Group, Apple Computer
Lines: 15



In trying to find the probability of a certain occurence, it is often
easier to try to find the probability that it does NOT occur. So, in
trying to find the probability that two card values X and Y occur
consecutively in a deck, assume X is at position i in the deck.  The
probability that a Y does NOT occur at position i-1 is p1=47/51 (the
number of non Y's over the number of cards left).  The probability
that a Y also does not occur at i+1 is p2=p1*46/50 (since we used up
a non-Y at i-1).  The probability that this happens for all 8 cards
is p2**8 which equals about .267.  Thus the probability that NO X
and Y will be consecutive is about 26.7%. (There is probably a slight
statistical variation at the beginning and end of the deck.)

Ken Doyle


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