Epictetus comments on My Bayesian Enlightenment - Less Wrong

25 Post author: Eliezer_Yudkowsky 05 October 2008 04:45PM

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Comment author: Epictetus 20 April 2015 07:19:15PM 1 point [-]

This is why I sometimes hate probability. The probabilities here strongly depend on how the family and boys are chosen.

If you took a list of families with exactly two children and threw out the ones that had no boys, then you'd find that of the remaining families, 1/3 have two boys.

If you took a list of boys who have exactly one sibling and asked how many of them had a brother, you'd get the answer 1/2.

The difference is whether the child is chosen at random. Even a minor change in the phrasing of the question can change the correct answer. Always be cautious with probability.