MATH: Bayesian story problem

From: Eliezer S. Yudkowsky (
Date: Sat Mar 29 2003 - 18:54:02 MST

A couple of #SL4ers have asked me for this, so I'm posting it to

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                
Research Fellow, Singularity Institute for Artificial Intelligence

This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:00:42 MDT