Now, the article I mentioned gives the same answer but asks the question in a different way. And I think that with the question they asked, you don't get this answer. I'd be interested to hear other people's views on it.
Their set up was:
Quote:
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Gary Foshee, a collector and designer of puzzles from Issaquah near Seattle walked to the lectern to present his talk. It consisted of the following three sentences: "I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"
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In my opinion, the probability here is still 1 in 3. My argument is that the information that one of his children is a boy born on a Tuesday doesn't actually give us any new information. The Tuesday is arbitrary, and could equally well have been any day of the week.
If we had a large number of fathers of two children one of which is a boy, all of them could all say similar statements (with different days of the week). This can't mean that 13/27ths of them had two boys.
Of course, 27 in 147
could say exactly what Gary said, and if we examined those 27 in 147, 13/27ths of them would have two boys.
But when volunteering a day of birth, only 21 in 147
would pick Tuesday (assuming that births are equally distributed among the days of the week, and that people with two boys don't have a preference for giving one day of the week over another). And of those 21 in 147, only 1/3rd would have two boys.
It is for this reason that I argue that the New Scientist article got it wrong - volunteering the day of birth doesn't get us a subset of the population with an 'excess' of two boys. Only by question and answer do we remove from consideration more single boy families than two boy families.