I'd stay with my original choice. It's 50/50 either way, so it doesn't really matter unless you have x-ray vision.
You are playing a game. A person (game host) shows you 3 boxes. 1 box contains £100, 2 others are empty. You need to choose one of the boxes. If the box you chosen contains the money you win.
Suppose you make a guess and point at some box. The game host instead of opening the box you just pointed at opens one of the other boxes and shows you that that box is empty. Then he asks "I'm going to give you a last chance to change your decision". So you can either stand by your original choice and point at the same box or choose the other one. What gives you better chances? (i.e. what are the chances you win if you choose the box you originally selected vs. the other box?)
I'd stay with my original choice. It's 50/50 either way, so it doesn't really matter unless you have x-ray vision.
Gikoku ハラカミ
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Don't think. Feel...
It's like a finger pointing to the moon.
Don't concentrate on the finger or you'll miss all that heavenly glory.
~Bruce Lee, Wing Chun.
Haha, morons.
edit: Think of it as two sides. There's your side, and the host side. When you choose one, the chance of having the hundred pounds in your side is 33% and his side is 66%. When he opens one of his and shows that it's empty and asks if you want to switch, you say yes, because his side still has a 66% chance of being the good box.
Edit: In case the first line seemed too offensive, know that I thought this at first as well.
Last edited by Brawny; 06-18-2009 at 09:22 PM.
Wow, I was actually leaning towards Adam's answer. Definitely thought the same as y'all at first though.
You guys should know that the answer isn't going to be that simple if Lewi posts an entire thread for it. :P
Damn, Adam beat me to it. Yes, it is statistically better to change your answer (I've seen this problem before, with doors instead of boxes).
I never add friend codes.
Originally Posted by AndThen?
I find this difficult to understand what you guys are saying?
3 boxes, 33% chance of the £100 being in any of them.
But if he shows you that 1 of the boxes are empty, then it's a 50% chance that your box is an empty one compared to the other 1..
So switching it would still make a 50% chance surely.
Unless you do all that 1/3 times a 1/2 statistics tree thing, but even that would come out the same?
I think I'm stupid, because I'd still stick with my first choice.
Oh yeah! I understand now. Thanks Napalm