>Well, you've got plenty of company -- I believe several hundred Mathematical PhDs also got it wrong, as well as thousands of others. Statisticians have a slight advantage, in that we are better trained in conditional probability. I tend to say that the 1/2 solution is not exactly wrong, it's just not the original problem, and some who gave that answer actually seemed to state the problem for which 1/2 is the right solution.
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>So a) it's a tricky problem even if you're tackling it correctly, (that is, how do the odds *change* if any door is selected and any other is shown with a goat), and
>b) it's quite easy to be answering the wrong problem, in one of two ways:
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>1) People fixate on, for example, door 1 always being chosen and door 2 always having the goat. It can be any combination of the doors, of course, which is a different problem.
>2) People treat the problem as a new one, in which there are only two doors, one with goat and one with prize, and forget the first 1/3 pick. As if a new problem just began, and of course 1/2 is the answer to that.

It calls to mind the misconception that people have that prior events affect the probability of future events. At the casino, the roulette wheel, if I have hit black 3 times in a row, the odds off hitting red on the next spin have increased. That's different than saying that if I have 4 spins, what are the odds that one of the spins will result in red.

Perhas, if the problem is stated in such a way that it is clear that it is a strategy that the player has adopted from the beginning, prior to opening any door, that would shed some light on the fact that we are dealing with probability over time.