Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site linus.UUCP
Path: utzoo!linus!brando
From: brando@linus.UUCP (Thom Brando)
Newsgroups: net.misc
Subject: Re: statistics problem solved simply (!)
Message-ID: <271@linus.UUCP>
Date: Fri, 19-Aug-83 13:19:39 EDT
Article-I.D.: linus.271
Posted: Fri Aug 19 13:19:39 1983
Date-Received: Fri, 19-Aug-83 16:33:36 EDT
Organization: MITRE Corp., Bedford MA
Lines: 18


OK, I answered 1/2 to the probability of having chosen the double-gold
cabinet, but I think the following demonstrates, sans intuition, why
2/3 is the "correct" answer:

Let A represent the event that you have chosen a drawer containing a
      gold coin, and let

    B represent the event that you have chosen the double-gold cabinet.

Then the probability that you have chosen the double-gold cabinet,
given that you have chosen a drawer containing a gold coin, is

		p(B|A) = p(BA) / p(A).

If you agree that p(A) = 3/6 = 1/2 and p(BA) = 1/3, then you should
also agree that p(B|A) = 2/3.  I only wish I had taken the time to
think before I "guessed" 1/2 (after all, it IS intuitive, isn't it!).