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Sir Kenyth · 12-14-2001, 10:48 AM

This is a little math riddle that was being discussed previously and submitted by Barry:

quote:

OK, heres a probability one for you. You are playing a game show and the host asks you to pick your prize. There are three doors you can pick and one of them has a prize behind it. The other two are empty (which, I admit, would be a prize to some people but not to most).
He asks you to guess so you pick one. He then opens one of the other doors to reveal nothing.
He asks you if you are still sure.
On the basis of pure probability should you stick or change?

This is a tricky little problem. Your fist instinct would be to say theres a 50/50 chance for the remaining two doors. Two doors, one choice, 50/50 chance. It's not that simple though. There's another factor to take into consideration. The trick is the fact that the game guy KNOWS which door the prize is behind. His choice of an empty door is NOT RANDOM. He has two doors to pick from and he knows which is empty. Therefore, since he HAS to pick an empty door, the door he DOES NOT PICK has a higher chance of being a prize door than your TOTALLY RANDOM guess. It's only because he knows where the prize is, see? His indirect choice has a higher probability than your direct choice because he's informed and you're not. Get it?

The thinking is a bit abstract on this one.

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NOTE: It appears I was wrong and that the original 50/50 argument holds. Read Legolas' reply further on and see how he mapped out the possible paths. 250 and I are bantering uselessly through most of this thread, but you might get a kick out of it!

12-14-2001, 10:48 AM	#1
Sir Kenyth Fzoul Chembryl Join Date: August 30, 2001 Location: somewhere Age: 55 Posts: 1,785	This is a little math riddle that was being discussed previously and submitted by Barry: quote: OK, heres a probability one for you. You are playing a game show and the host asks you to pick your prize. There are three doors you can pick and one of them has a prize behind it. The other two are empty (which, I admit, would be a prize to some people but not to most). He asks you to guess so you pick one. He then opens one of the other doors to reveal nothing. He asks you if you are still sure. On the basis of pure probability should you stick or change? This is a tricky little problem. Your fist instinct would be to say theres a 50/50 chance for the remaining two doors. Two doors, one choice, 50/50 chance. It's not that simple though. There's another factor to take into consideration. The trick is the fact that the game guy KNOWS which door the prize is behind. His choice of an empty door is NOT RANDOM. He has two doors to pick from and he knows which is empty. Therefore, since he HAS to pick an empty door, the door he DOES NOT PICK has a higher chance of being a prize door than your TOTALLY RANDOM guess. It's only because he knows where the prize is, see? His indirect choice has a higher probability than your direct choice because he's informed and you're not. Get it? The thinking is a bit abstract on this one. --------------------- NOTE: It appears I was wrong and that the original 50/50 argument holds. Read Legolas' reply further on and see how he mapped out the possible paths. 250 and I are bantering uselessly through most of this thread, but you might get a kick out of it! __________________ Master Barbsman and wielder of the razor wit!<br /><br />There are dark angels among us. They present themselves in shining raiment but there is, in their hearts, the blackness of the abyss.