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Emile comments on Bayes' Theorem Illustrated (My Way) - Less Wrong
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I get that assuming that genders and days of the week are equiprobable, of all the people with exactly two children, at least one of whom is a boy born on a Tuesday, 13/27 have two boys.
True, but if you go around asking people-with-two-chidren-at-least-one-of-which-is-a-boy "Select one of your sons at random, and tell me the day of the week on which he was born", among those who answer "Tuesday", one-third will have two boys.
(for a sufficiently large set of people-with-two-chidren-at-least-one-of-which-is-a-boy who answer your question instead of giving you a weird look)
I'm just saying that the article used an imprecise formulation, that could be interpreted in different ways - especially the bit "if you supply the extra information that the boy was born on a Tuesday", which is why asking questions the way you did is better.