

Russel's Paradox in Probability - DanielRibeiro
http://beust.com/weblog/2011/10/27/probability-quiz/comment-page-1/

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pmiller2
This commenter has the right answer. ->
[http://beust.com/weblog/2011/10/27/probability-
quiz/comment-...](http://beust.com/weblog/2011/10/27/probability-quiz/comment-
page-1/#comment-12590)

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
Meh. 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%)."

