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From: mcewan@uiucdcs.UUCP
Newsgroups: net.math
Subject: Re: Simple Monty Hall - (nf)
Message-ID: <3272@uiucdcs.UUCP>
Date: Sun, 16-Oct-83 23:27:22 EDT
Article-I.D.: uiucdcs.3272
Posted: Sun Oct 16 23:27:22 1983
Date-Received: Thu, 20-Oct-83 03:24:27 EDT
Lines: 23

#R:qubix:-59200:uiucdcs:28200027:000:708
uiucdcs!mcewan    Oct 16 11:09:00 1983

	Let's make this simple by enumeration. Possibilities:
	(> == I pick; M == what MH shows)
	
	> B	M B	  G	-> Gain by switching
	M B	> B	  G	-> Gain by switching
	M B	  B	> G	-> Lose by switching
	  B	M B	> G	-> Lose by switching
	
	What is being overlooked (cabinet/drawer/coin problem again) is that I
	can choose from TWO bad doors, which are not identical!!!
	This move the odds from 2/1 (p = 2/3) to 2/2 (p = 1/2).
	Can I make it any simpler?
/* ---------- */

You've already made it too simple. The problem with this is that the four
cases shown are NOT equally probable. The probabilities are 1/3, 1/3, 1/6
and 1/6 respectively => P(gain by switching) = 2/3.

				Scott McEwan
				pur-ee!uiucdcs!mcewan