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MaryCh 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 2 points [-]

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.

Comment author: MaryCh 22 July 2017 04:14:40PM 0 points [-]

Why 1/3?

Comment author: arundelo 25 July 2017 10:33:42AM *  1 point [-]

Families with exactly two children:

| oldest | youngest |
+--------|----------|
| boy... | boy..... | two boys
| boy... | girl.... | one boy
| girl.. | boy..... | one boy
| girl.. | girl.... | no boys
Comment author: MaryCh 25 July 2017 03:32:51PM 0 points [-]

Thank you. I should have realised that.

(And is it not weird, how two questions of the same, well, validity, give two different answers and perhaps - in a situation, where it matters - lead to different formulations?)