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Fyrius comments on Bayes' Theorem Illustrated (My Way) - Less Wrong
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Wonderful. Are you aware of the Tuesday Boy problem? I think it could have been a more impressive second example.
(The intended interpretation is that I have two children, and at least one of them is a boy-born-on-a-Tuesday.)
I found it here: Magic numbers: A meeting of mathemagical tricksters
Note before you start calculating this: There's a distinction between the "first" and the "second" child made in the article. To avoid the risk of having to calculate all over again, take this into account if you want to compare your results to theirs.
I calculated the probability without knowing this, so that I just counted BG and GB as one scenario, where there's one girl and one boy. That means that without the Tuesday fact the probability of another boy is 1/2, not 1/3.
(I ended up at a posterior probability of 2/3, by the way.)