Author: fca
Date: 18:41:36 08/16/98
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On August 16, 1998 at 21:08:29, Bruce Moreland wrote: >>>Describe a method wherein with nothing more than a single ordinary coin you can >>>generate a probability of exactly 1/3. >How about this. I will call a "failure" a case where you are in the 2/3 region, >and a success a case where you are in the 1/3 region. > >1. Flip the coin. Heads is a failure, done. >2. Flip the coin. Heads is a success, done. >3. Back to 1. Sure, also works, and is perhaps more mathematically complex than mine as the proof involves summing a geometric progression... P(success) = 1/2 * 1/2 * ( 1 + 1/4 + 1/16 + 1/64 +..... which, after some rearranging, subtraction etc. (or formula use) = (1/4) / (1 - 1/4) = 1/3 while mine merely involved considering the 3 possible outcomes (ignoring HH) of two consecutive tosses (the rest was just program babble) To me, the simpler method is the one relying on the simpler principle (and therefore having a simpler proof). - eleusis theory. There were elements of elegance in both. >bruce Kind regards fca PS: Please do not disregard the other tasty morsels left for you ;-)
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