From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sun Jul 06 2003 - 00:48:09 MDT
Eliezer S. Yudkowsky wrote:
> 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.)
PS:
3. Using orthodox methods and an expensive statistics program, calculate
the probability that, if the hypothesis "I am looking at the red barrel is
correct", you will see 7 or more red tokens in ten samples. Explain why
this number is actively harmful to genuine statistical understanding in
twenty-five words or less.
-- Eliezer S. Yudkowsky http://singinst.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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