You have exactly the same odds on picking any given box.
There is 33% chance you will pick box A
there is also 33% chance you will pick box B
So there is the same chance that you picked the box he leaves you as there is of you picking the box you did.
Sure. It's just not 50/50. The only thing that makes this even slightly confusing to anyone is the stipulation that the game show host will open every door that is empty except one and the one that you chose. If there were 50 Billion doors and he opened 49,999,999,998 of them, would you find it equally likely that you picked the one in 50 billion door with your one guess or that he opened all but the correct door?
Obviously your chances of picking the correct door out of two is 50/50. There's no point at all in stating this. It's a given. That's not the situation though. The situation is you choose 1, then the host opens ALL other doors that aren't winners. The confusing part of the given problem is that that all of them happens to be 1.
Edited, Apr 1st 2008 8:59pm by Smasharoo
____________________________
Disclaimer:
To make a long story short, I don't take any responsibility for anything I post here. It's not news, it's not truth, it's not serious. It's parody. It's satire. It's bitter. It's angsty. Your mother's a *****. You like to jack off dogs. That's right, you heard me. You like to grab that dog by the bone and rub it like a ski pole. Your dad? Gay. Your priest? Straight. **** off and let me post. It's not true, it's all in good fun. Now go away.