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It seems to me that the statement of the problem in the Wikipedia article (taken, as I understand it, from the original question sent to her) is almost, but not quite well specified. It was:
Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?
To get the (presumed) original intent, it must additionally be made clear that the host *would* have opened a door with a goat behind it regardless of your first choice.