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From: mcewan@uiucdcs.UUCP (mcewan )
Newsgroups: net.math
Subject: Re: YAST (Yet Another Statistics Problem - (nf)
Message-ID: <3015@uiucdcs.UUCP>
Date: Wed, 28-Sep-83 22:31:30 EDT
Article-I.D.: uiucdcs.3015
Posted: Wed Sep 28 22:31:30 1983
Date-Received: Fri, 30-Sep-83 20:43:06 EDT
Lines: 23

#R:utcsrgv:-228700:uiucdcs:28200019:000:970
uiucdcs!mcewan    Sep 28 11:22:00 1983

	You've made it as a contestant on Let's Make a Deal.
	
	Monty shows you three doors, only one of which has a good
	prize behind it.  You make your choice and Monty opens one
	of the doors with a bad prize behind it (as he always does).  
	He now asks you whether you would like to switch to the 
	remaining door.  The million dollar question is.... 
	should you switch or does it matter??

Switch. The third door has twice the probability of having the good
prize as the door you chose. When you made your choice, each door had
a 1/3 probability of having the good prize. Regardless of which door
you chose, Monty will show you a door with a bad prize (if you chose
a bad door, he shows you the other one; if you chose the good door,
he chooses a door at random), so this tells you nothing about the
probability of the door you chose - thus the probability stays 1/3.
Therefore, the probability of the last door having the good prize is
1-1/3 = 2/3.

					Scott McEwan