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From: leichter@yale-com.UUCP (Jerry Leichter)
Newsgroups: net.math
Subject: Re: YAST (Yet Another Statistics Problem)
Message-ID: <2184@yale-com.UUCP>
Date: Mon, 17-Oct-83 15:36:43 EDT
Article-I.D.: yale-com.2184
Posted: Mon Oct 17 15:36:43 1983
Date-Received: Tue, 18-Oct-83 02:57:18 EDT
References: trw-unix.445
Lines: 19

Here is an interesting argument, due to Dave Wittenberg, that shows that
switching doors DOES gain:

Suppose you follow a different algorithm:  Choose a door at random.  Monty
shows you a "bad door".  Flip a fair coin; if it is heads, keep the door
you already have; if it is tails, switch.  Now what are your chances?
Well, the coin washes out any information from your first choice.  It makes
no difference what the original probabilities were.  After Monty shows you
a bad door, you are ALWAYS in the position of having two doors available to
you, one good, one bad.  The coin toss as described is indistinguishable
from a fair coin toos to choose on of these two doors.  Hence, this
strategy gives you a 50% chance of winning, while always keeping the
original door gives you a 1/3 chance.  So switching CAN improve your
chances...and a detailed argument for 2/3 if you always switch is plausible.

The case analysis someone sent out is incorrect because it assume each of
the four cases listed is equally probable, which is not the case.
							-- Jerry
					decvax!yale-comix!leichter leichter@yale