In that respect it reminds me of the old "Monty Hall" question about whether you should switch your selection when they show you where the bad "prize" is, but it's really just the opposite of that effect: Really, what IS the difference between "boy/girl" and "girl/boy?" What do the different designations denote? What makes a pair of children "boy/girl" AND precludes them being "girl/boy"? I don't see how those are different outcomes, unless we're considering birth order, but we aren't told whether the eldest or youngest child was the boy born on Tuesday, so, presumably, order is not a factor.

In terms of the articles stated potential outcomes, the first two are identical, simply a case of the old "I have two coins totalling thirty cents and one of them is not a quarter; what are they?" A quarter and a nickel, because only ONE of them is not a quarter. Likewise the last two outcomes are essentially the same, unless we take "one is a boy born on Tuesday" to LITERALLY mean ONLY one boy was born on Tuesday (again, thinking back to the quarter question. ) If we are, in fact, to take the statement literally, there are 6 ways another boy could be born (because if another were born on Tuesday that would be TWO, not one ) and 7 ways a girl could be, and I can't see any reason why the correct answer is not 6/13.