Re: [Phys-l] Monty Hall problem

[William Robertson <wrobert9@ix.netcom.com>]

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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