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Russel's Paradox in Probability
- pmiller2 15y agoThis commenter has the right answer. -> http://beust.com/weblog/2011/10/27/probability-quiz/comment-page-1/#comment-12590 http://beust.com/weblog/2011/10/27/probability-quiz/comment-... The question is phrased such that most people will immediately assume the distribution from which we choose an answer is uniform over {A, B, C, D}. If, indeed, we choose each answer with equal probability 1/4, then none of the answers can be correct. This is not a paradox! It's simply a proof by contradiction that the distribution from which we select our answer "at random" cannot be uniform over all the choices. The problem is clearly with the phrase "at random," which is ambiguous in a mathematical context, but, in popular meaning is equivalent to "uniformly at random."
- waqf 15y agoMeh. If you think of randomness as information entropy, then the uniform distribution is the unique most random distribution. So you can argue, "when you said at random, it's reasonable to assume you meant completely at random (i.e. in the most random way) not just somewhat at random (e.g. 99.9%/0.1%/0%/0%)."