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From: larry@grkermit.UUCP (Larry Kolodney)
Newsgroups: net.math
Subject: Re: Why is it 2/3?????
Message-ID: <617@grkermit.UUCP>
Date: Wed, 24-Aug-83 10:49:16 EDT
Article-I.D.: grkermit.617
Posted: Wed Aug 24 10:49:16 1983
Date-Received: Wed, 24-Aug-83 17:13:22 EDT
References: <304@rdin.UUCP>
Organization: GenRad Inc., Concord, MA
Lines: 46

OK.  ONE MORE TIME AND THEN I QUIT.

	From sarah@rdin:
	
	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.

~~~~~~~~`
Just refer to the Article about the shredded National Enquirer.

Or better, here's actually an intuitive way to think about it.

Lets say we pick a coin at random from one of the six drawers, before
we do anything else.  What is the prob.  that IT is gold.  I hope you
said 1/2, because there are 3 of each type of coin.
After we pick the gold coin, we have to pick another coin at random.
Wouldn't you assume that since we've already eliminated two silver and
only one gold coin the odds should be better for the gold coin?

If yo agree with this than 1/2 is obviously wrong!  Now, why 2/3.  Well
you have 2wice as many gold coins as silver left, so 2/3 is it!

The crux of the argument is to convince yourself that choosing the
drawer after the first coin toss is just as random as before.  Since
either DRESSER is just as likely, they are interchangable, and picking
the drawer in the same dresser is just like picking any of the drawers
from one of the dressers with a gold coin in it.

Okay?
-- 
Larry Kolodney (The Devil's Advocate)
{linus decvax}!genrad!grkermit!larry
(ARPA)  rms.g.lkk@mit-ai