Jon Gabriel wrote:
>
> >From: Bryon Daly <[EMAIL PROTECTED]>
> >Reply-To: Killer Bs Discussion <[EMAIL PROTECTED]>
> >To: Brin List <[EMAIL PROTECTED]>
> >Subject: Another prisoner's dilemma (the Monty Hall question)
> >Date: Fri, 14 Feb 2003 15:40:07 -0500
> >
> >This isn't really a puzzler like the last one, but I find the answer
> >interesting...
> >
> >The warder comes to a prisoner's cell with 3 boxes and says: "I've placed a
> >key in one of these 3 boxes. If you can pick the box it is in, you may go
> >free".
> >
> >The prisoner picks a box, then the warden selects a different one, opens
> >it to
> >reveal it is empty, and then says: "Would you like to switch your chosen
> >box
> >with the remaining unopened box?".
> >
> >You can assume the warden would have offered the switch regardless of
> >which box the prisoner had chosen (ie: key or not). Should the prisoner
> >switch boxes? What are his odds of freedom if he does?
> >
> >-Bry
> >
>
> Yes, he should switch boxes. Although I know the answer, I've never
> understood it.
>
> There is a 1/3 probability of getting the key with the box you have. After
> the warden shows you his box is empty, the probability of it being in the
> other box becomes 2/3. What I don't understand is why it doesn't now become
> 1/2.
>
> Perhaps with that as a starting point, someone could provide a more
> understandable explanation?
OK, say you've got boxes A, B and C.
You pick box A. There's a 2/3 chance that the key is *not* in box A. When
box B or C is opened and the key is shown not to be in that box, there's
still a 2/3 chance that the key is *not* in box A, so it's a 2/3 chance that
it *is* in the box that is neither A nor opened. Opening the box didn't
change anything about box A.
Does that help?
Julia
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