From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sun Jul 06 2003 - 00:25:31 MDT
In front of me is one barrel containing 25 red tokens and 75 blue tokens,
and another barrel containing 75 red tokens and 75 blue tokens. I select
a barrel at random (i.e., by flipping a fair coin). Sampling a random
token with replacement, you observe the following sequence of draws:
R, B, R, R, B, B, R, R, R, R. (Total of 3 blues, 7 reds.)
1. After repeatedly revising your probability to take each of these
observations into account, what is your estimated chance that the barrel
is the one containing mostly blue tokens?
2. Explain how you were able to solve this problem entirely in your head
in less than thirty seconds.
(Adapted from Ward Edwards.)
-- Eliezer S. Yudkowsky http://singinst.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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