Your assumptions were almost on the mark, but not quite…
Here is the original question again:
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 No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
The basic point of this question is two bads and one good, and one of the doors is opened and you are asked if you want to change your choice. No where in this question is it stated that the host had the choice to display a door, only that he knew what was behind them. Neither is it much of a point NOT to open a door, as there is no change to the equation, and no reason for the person to switch, or to even ask the question, is there? The fact that the door was opened is the whole point of the question - does revealing one of the doors change your odds of having picked the car? Of course not.
I think this time there was too much read into the simple question.
University of Washington