You're on a game show. There are three doors before you, behind one of which is a car, and behind the other two are goats. You can pick one door, and you get whatever's behind that door, be it car or goat. Now, before the host opens your chosen door, he opens one of the other doors that contains a goat (for there will always be an unchosen door that contains a goat). Upon this revelation, he then gives you the opportunity to switch your chosen door for the other, unopened door (i.e., you win whatever is behind the other door instead of the one you had previously chosen).
The questions are these: Should you switch? Why, or why not?
The host knows in advance where the cars and goats are, while you do not. Your aim is to win a car. There is no way to know what is behind a door without opening it.
As always, if you know the answer to this puzzle already, don't spoil it! Or, if you must, use spoiler tags! (See the past few pages for how to do them). You get reps if you can not only give the right answer, but explain why. You may also get a cookie.
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