# MATH: Bayesian story problem

From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sat Mar 29 2003 - 18:54:02 MST

A couple of #SL4ers have asked me for this, so I'm posting it to
SL4-the-mailing-list:

Suppose you have a large barrel containing a number of plastic eggs. Some
eggs contain pearls, the rest contain nothing. Some eggs are painted
blue, the rest are painted red. Suppose that 40% of the eggs are painted
blue, 5/13 of the eggs containing pearls are painted blue, and 20% of the
eggs are both empty and painted red. What is the probability that an egg
painted blue contains a pearl?

As a check on your calculations, the likelihood that a red egg is empty,
divided by the likelihood that an egg contains a pearl, equals
approximately .51. To use this information in the problem, of course,
would be cheating.

```--
Eliezer S. Yudkowsky                          http://intelligence.org/
Research Fellow, Singularity Institute for Artificial Intelligence
```

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