No idea why this problem came into my head, but it did so I was having a little browse.
But anyway, what I'm thinking is that ultimately, you're not making a decision until there's two boxes; one winner, one loser. Is it not irrelevant which box you pick first?
The diagram that you posted Kyle, should there not be 4 choices? Option 1 could be split into two as there's two possibilities for which un-chosen, empty cup to remove. That would make it a 1/2.
I've always leant towards it being a 1/3, but for some reason I can't decide now, which annoys me.
Probability aside, if this situation ever comes up, it'll be on Wheel of Fortune or some other yawntastic game show or a street-side entertainer. This will be only ONE instance, in which probability doesn't play a factor or matter a shit in my opinion. My advice would be to go with your gut instinct and keep the first one you picked.
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I think my original way of figuring this out was flawed, even if it was correct. I'm not sure I completely understand.. do you have a 2/3 chance at the end solely because one of the cups has been shown empty?
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Originally Posted by AndThen?
Excellent. I was hoping to be completely proved wrong, because I knew 2/3 was correct but I'd been looking for proof that switching is best, but everywhere I had looked people couldn't completely validate their answer.
It's all the same to me, because while the chances of success may theoretically change, the item within the box never changes boxes from start to finish. So while your chances get better or worse it's still all down to chance, no matter how many you're choosing from. Unless you're psychic.
Bloody hell, never thought of it like that. Interesting...
I guess I should have taken statistics in my fifth year of maths instead of stopping at four years.
Oh, I get it. Because the box he removes can never be the box that you originally chose, so the yet-to-be-chosen box has 2/3 chance of being correct?
That took me forever to comprehend, and part of me still wants to believe that it's simply 50/50, but it's okay because I have yet to take statistics.
EDIT: That was a really interesting explanation, Napalm. That you want to originally pick a bad box so that you can switch to the good.
Last edited by LevesqueIsKing; 06-22-2009 at 08:53 PM.
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