Gary Paveza writes:

>Every time I hear this one I scratch my head in confusion.
>
>At the beginning, you have a 1 in 3 chance of guessing the right door.

Here's a copy of the response I wrote last time (see
<http://www.optc.com/chemed-l-thread/Thread1980.html> for the full
discussion):

>I probably shouldn't answer this, but it's more fun than what I *should*
>be doing. :-)
>
>When you first choose one of the three doors, there's a 1/3 chance that
>you're standing on the wealth beyond dreams of avarice (WBDOA). Most
>people focus on this, which is the source of the difficulty. But there's
>a 2/3 chance that you're standing on a goat, and it's easier to
>understand the reasoning from that perspective.
>
>When Monty shows you a goat (remember, he will *never* show the WBDOA),
>that original 2/3 doesn't change, because opening the curtain doesn't
>change the state of your knowledge before you chose: there's still a 2/3
>chance that you're standing on a goat. But since Monty has now shown you
>a goat, that means that there's now a 2/3 chance that the door you didn't
>pick is the one with the WBDOA.
>
>It's easy to think that when Monty exposes the goat, the chances are now
>50/50. The reason it's not that way is that Monty's choice wasn't random:
>he deliberately avoided the door with the WBDOA. If Monty had opened a
>random door and exposed a goat (which would happen half the time), then
>it really wouldn't matter whether you switched.

This is another case where it's easiest to see the reasoning if you list
all the possibilities.

-- Bruce



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