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From: sarah@rdin.UUCP (sarah)
Newsgroups: net.math
Subject: Why is it 2/3?????
Message-ID: <304@rdin.UUCP>
Date: Tue, 23-Aug-83 11:40:51 EDT
Article-I.D.: rdin.304
Posted: Tue Aug 23 11:40:51 1983
Date-Received: Thu, 25-Aug-83 23:36:46 EDT
Lines: 57

c(FbiLhLhD*@iQhL


 Here is the nasty gold/silver problem, exactly as it appeared:


   Here goes:  you are in a room with three cabinets, each of which has
   two drawers.  One cabinet has a gold coin in each drawer.  Another
   has a silver coin in each drawer.  The third has a gold coin in one
   drawer and a silver coin in the other.
   
   You pick a cabinet at random and open a random drawer.  It contains
   a gold coin.  What is the probability that the other drawer of that
   same cabinet contains a gold coin?


 OK, folks, I've read your solutions claiming to prove that the probability
 is 2/3.  However, this answer seems to rest on one or both of the following
 assumptions:
   
   1)  Any of the three remaining drawers (having tossed out the SS cabinet) 
       can be chosen.

   2)  The gold coin you know about was *not* necessarily the first one
       you chose.


 When as a matter of fact, Larry Kolodney states:

   So, there are three gold coins.  Since we have an equal chance of 
   choosing any one of them, if we do choose one it is equally likely
   that it is the one in the silver gold cabinet, or that it is one of 
   the two in the gold gold cabinet. {He then continues on to support
   the 2/3 answer.}

The problem with the 2/3 answer is that once we have that gold coin in our
grubby little paws, we have reduced the problem to two cabinets (not three
remaining drawers).  If the problem had asked about the probability before
we knew we had one gold coin, or if we were free to choose from the three
remaining drawers, the answer would be different.  However, by choosing a
gold coin, we know:

   1) The silver cabinet is out of the question.

   2) The one remaining drawer we must open to determine which cabinet 
      we have chosen must contain either a gold coin or a silver coin.

 The probability associated with picking a gold coin in the first place
 is *not* part of the original question as stated.  It is a *given* that
 the gold coin is chosen.

 Can you please explain yourself clearly once more for the benefit of all
 us confused people out here?

                                       Sarah Groves
				       New York
				       philabs!rdin!sarah