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Re: [Phys-l] Monty Hall problem



You have just identified the key question: it is critical that the rules be spelled out in advance with no ambiguity: Monty Hall has to tell you IN ADVANCE that he will be making this offer EVERY TIME. In that case, clearly you should switch. But without that point, it's anyones guess: I suspect that some who would not switch suspect what you have suggested: that sneaky host is trying to lure me into giving up what he knows was the winning choice.
________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] on behalf of William Robertson [wrobert9@ix.netcom.com]
Sent: Wednesday, January 05, 2011 5:18 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Monty Hall problem

So you would hold onto the door with a 1 in million chance of winning
and not choose the door with 999,999 chances in a million of winning?
Or are you saying that the only reason the host opened all those doors
was because he knew you had already chosen the winner?

Bill




On Jan 5, 2011, at 3:00 PM, John Mallinckrodt wrote:

It's also interesting to consider Marilyn's original "explanation" a
little more closely. According to the seemingly authoritative
source that John Denker quoted, the original question and her
original answer were

Suppose you're on a game show, and you're given the choice of three
doors. Behind one door is a car, behind the others, goats. You pick
a door, say #1, and the host, who knows what's behind the doors,
opens another door, say #3, which has a goat. He says to you, "Do
you want to pick door #2?" Is it to your advantage to switch your
choice of doors?

Craig F. Whitaker
Columbia, Maryland

Yes; you should switch. The first door has a 1/3 chance of winning,
but the second door has a 2/3 chance. Here's a good way to
visualize what happened. Suppose there are a million doors, and you
pick door #1. Then the host, who knows what's behind the doors and
will always avoid the one with the prize, opens them all except
door #777,777. You'd switch to that door pretty fast, wouldn't you?

This "visualization" may sound pretty compelling, but what if we
further suppose that the prize was a billion dollars. Would you
switch? Without some pretty solid additional information, I sure
wouldn't.

John Mallinckrodt
Cal Poly Pomona
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l