Quote:
Originally Posted by chillrob
I think the way the Monte Hall program is usually expressed does not give you enough info; you have to make assumptions about how the guy is picking the doors, that are not typically presented, in order to understand it correctly.
Basically you have to assume the host always deliberately picks a goat to show you...that is not typically stated in the problem. Possibly that was the way it was done on the old TV show and someone familiar with the show would have gotten it, but as someone who never watched the show, it was very confusing until I realized that.
This is incorrect, and shows you don't understand the problem (which is normal, so no shame in it). He can't show you the winner, because you'd just pick that door now that he's revealed it. After you pick a door, he has two to show you (and must show one) and thus can always show a goat. Given that the host must show you the contents of a door, his only play is to use his knowledge to show a goat.
The problem isn't about confusion of the rules, the problem is that most people have horrible intuitive feel for conditional probability.
BTW, this picture should clearly explain the reason switching gives 2/3 of a chance of winning.