> From: "anonymous" <anonpy104@psy.soton.ac.uk>
>
> I can understand why some people may think the last door has
> 1/3 chance. However I still disagree, believing there is
> only 1/2 chance, as do most of my non-psychology friends.
>
> Therefore, as I can understand why other people think it's
> 1/3 BUT I cannot understand why that is the solution in my
> own mind. Does this mean the Monte Hall problem is
> cognitively penetrable to them, but cognitively impenetrable
> to me?
It doesn't mean the problem is not cognitively penetrable; some people
just take more convincing than others!
How about this:
The three door are A, B & C.
Each has a 1/3 chance.
Suppose you always pick A: A will always win about 1/3 of the time, and
NOT-A (= B & C) will always win 2/3 of the time.
You are not allowed to pick two doors at a time, so Monty Hall makes it
easier for you: he always shows you which of B & C it ISN'T.
Now you know A wins 1/3 of the time and loses 2/3 of the time.
You also know B & C wins 2/3 of the time.
You agree it's better to choose B & C every time, rather than A.
Well, by revealing which of B & C is empty every time, Monty allows you
to choose B & C every time, by eliminating whichever one of them is
empty.
Think of switching from A to not-A as a switch to B & C with the extra
clue that whichever of B & C has no prize will always be revealed to
you each time by Monte Hall.
That's exactly like getting to choose both of them every time, hence it
will always win 2/3 of the time.
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