[knappa]

You could definitely replace "Tuesday" with something like that and part of the pedagogical purpose of the problem is for people to question this. The actual effect comes from not distinguishing the boys. That increases the likelihood that at least one of them will be born on any particular day, upweighing the likelihood that there are larger numbers of boys. i.e. You just get, on average, better coverage of boys-born-on-Tuesday when there are more boys.

[FabHK]

Well, "born on a day" would not convey any information unless it means "during daytime". If that has probability 1/2, the answer would be 3/7. With Tuesday (or, indeed, any other weekday, with probability 1/7), it is 13/27.