Re: Monty Hall

From: Harnad, Stevan (
Date: Fri Feb 28 1997 - 20:47:04 GMT

> From: "anonymous" <>
> 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

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.

This archive was generated by hypermail 2b30 : Tue Feb 13 2001 - 16:23:51 GMT