Fun Mathy Type Riddles

[Fireball]

Ohhhh see this whole time I must have read it wrong because I was under the idea that the door we picked was opened and revealed a goat. So we still don't know what is behind our door then...

Yeah the problem states that:

1)  You pick a door - you do not know what is behind it.
2)  The game host picks one of the other two doors which you did not pick, and shows you what is behind it.  (He always picks a goat of course.)
3)  Then he offers you the choice between staying with your original pick (whose contents you still don't know) - or - the one remaining, unopened door (whose contents you also do not know).
4)  So do you stay with your original choice or switch?

You have to know that there is always only one door with a good prize behind it.  So the game host can always show you a 'goat' (bad prize) behind one of the two doors you didn't pick.

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Another way FF explained it was to ask what you would do if the game contained more than three doors and always showed you 'goats' behind all the doors but one of the those you didn't pick.  So if there were 4 doors, he'd expose goats behind 2 and ask if you wanted to switch.  If there were 100, he'd show you 98 goats and then ask if you want to switch to the one he didn't show you.  Is there any number of starting doors which would lead you to want to switch after the game host showed you goats behind all but one door?

Hey, I remember feeling very strongly that the probability was equal (1/2) whether you switched or not.  That initial intuition is so strong that it can prevent you from investigating other ways to confirm your answer.  Good luck.

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Even professional mathematicians can mix this up. A bunch of them chewed Marylin Vos Savant up over her (correct) analysis many a moon ago, when she published it in her "Ask Marylin" column.