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Re^4: Spooky math problemby tilly (Archbishop) 
on Sep 02, 2005 at 02:17 UTC ( #488531=note: print w/ replies, xml )  Need Help?? 
If you want to throw around ad hominem insults, nobody can stop you. That doesn't make them justified. For the record, I am very aware that one cannot define things like expected values and probabilities without a probability distribution. I am also painfully aware that many things that look like they might reasonably make probability distributions (eg a uniform distribution on the real numbers), don't. But the problem that I'm giving here can readily be precisely worded in a way that entirely avoids those issues. Here is the precise wording: Suppose that you have 2 different numbers x and y in 2 envelopes, written down in decimal form. Let us define the following experiment. You will randomly hand me one of your two envelopes, I will look at it, and I will tell you whether I think you handed me the larger. Is there an algorithm that I can use, which guarantees that the probability of my being right, given x and y (which I do not know) and my algorithm, is strictly better than 50%?Note the following critical details:
Now I won't go through the full reasoning again here. But if you're interested, this was discussed extensively on sci.math over a decade ago. For a particularly clear explanation, see this post by Bently Preece.
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