- 19 Apr '03 20:03You're on a tv game show with a $1 million prize. The prize is behind one of three doors.

You choose door #1.

The host says: ok, you've chosen door #1. Now I'm going to tell you the prize is NOT behind door #3! Would you like to stay with your choice, or switch to door #2?

What's your best choice?

- 19 Apr '03 23:51

I'm assuming here that the numbers 1 and 3 are arbitrary (otherwise why would you ever choose 3?) and that probabilites are equal, in which case I disagree. You have a 1/3 chance of picking the correct door first time. Clearly if you switch, you lose. However there's a 2/3 chance that you've picked the wrong one. The host then eliminates the other wrong one, so if you switch, you're guaranteed to win.*Originally posted by Weird Al***stay w/ #1**

In conclusion: if you stick, you have a 1/3 chance of winning. If you switch, you have a 2/3 chance of winning. I think this problem has been posted here before. - 20 Apr '03 01:40

People always get this wrong. I use this example in my intro. class to show that we may not be as rational as we all take ourselves to be. Humans are notoriously poor preformers when it comes to probability. Although you should switch doors, people generally think "there's still just the two options available, so now my chances must be 50/50".*Originally posted by Acolyte***I'm assuming here that the numbers 1 and 3 are arbitrary (otherwise why would you ever choose 3?) and that probabilites are equal, in which case I disagree. You have a 1/3 chance of picking the correct door first time. Clearly if you switch, you lose. However there's a 2/3 chance that you've picked the wrong one. The host then eliminates the other wro ...[text shortened]... you switch, you have a 2/3 chance of winning. I think this problem has been posted here before.** - 21 Apr '03 21:54"Argument is argument. You cannot help paying regard to their arguments, if they are good. If it were testimony you might disregard it&#8230;Testimony is like an arrow shot from a long bow; the force of it depends on the strength of the hand that draws it. Argument is like an arrow from a crossbow, which has equal force though shot by a child."

Intelligence is recognizing the accuracy of this statement.

Knowledge is knowing who said it.