From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Mon Oct 28 2002 - 16:08:43 MST
Suppose that we flip a fair coin 20 times, and that a biased sampling
procedure then randomly selects 5 coinflips from the set of coinflips that
came up heads and reports on those coinflips; if there aren't 5 coinflips
that came up heads, the biased sampling procedure reports all available
heads and enough randomly selected tails to make up the gap.
Suppose the biased sampling procedure reports that the first, sixth,
eleventh, fifteenth, and eighteenth flips came up heads. Is there a
simple general formula for calculating the probability that any given
other coinflip came up tails? Clearly the probability is greater than
50%, but by how much?
(I don't know the answer to this one; it's posed as a genuine math
question, not a math problem.)
-- Eliezer S. Yudkowsky http://singinst.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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