Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10 5/3/83; site psuvax.UUCP
Path: utzoo!linus!decvax!harpo!eagle!allegra!psuvax!mitchell
From: mitchell@psuvax.UUCP
Newsgroups: net.math
Subject: Re: Why is it 2/3?????
Message-ID: <200@psuvax.UUCP>
Date: Wed, 24-Aug-83 11:32:42 EDT
Article-I.D.: psuvax.200
Posted: Wed Aug 24 11:32:42 1983
Date-Received: Wed, 24-Aug-83 19:44:34 EDT
References: <304@rdin.UUCP>
Organization: Penn. State Univ.
Lines: 15

We have three cabnets, each with three drawers.  
We pick a drawer (or equivalently a coin) at random and find it is gold.  
There are three possibilities: either of the drawers of the gold-gold cabinet and the gold drawer
of the gold-silver cabinet.  In two of the cases (the drawers of the gold-gold cabinet)
the other drawer is gold; in one case (the silver-gold cabinet)
the other drawer is silver.  Therefor the probibility is 2/3 that the other drawer is gold.

This is trickier to think about if you think of first choosing the cabinet and then the drawer.
One way to do this is think of making 1 of 3 equally likely choices, and after that 1 of 2, making 6 equally likely choices and leaving us with the first analysis.

Incidentally, the arogance of some of the articals on this issue
has been so obnoxious as to leave it irrelevant whether or not they are correct.
One of the most obnoxious I reread carefully and still couldn't decide
what answer he was claiming, far less his reasoning for it.