Hence, as in Birdeyes first example, saying boy/girl is different from girl/boy is like saying "no, I didn't roll a four and a three, I rolled a three and a four. "

Again, the only way you don't end up with the same 50/50 shot he did (and the way I initially looked at it was that by stating one child is a boy you've made it a determined event, so you're down to ONE childs possible genders: 50/50) is if we take "One is a boy born on a Tuesday" to mean "they are not BOTH boys born on a Tuesday, only one of them is. " Again, in that case there's slightly less than a fifty percent chance the other one is a boy, since a child of either gender can be born on any day of the week (making 7 days for 2 genders, a total of 14) EXCEPT Tuesday, because one and only one boy was already born on Tuesday. Six days on which a boy can be born plus seven days on which a girl can be make a total of thirteen outcomes, of which six are boys: 6/13.

However, even that assumes something not explicitly stated in the problem; it could be "one of them is a boy born on Tuesday, and so is the other one" and we're back to 50/50.

The problem here is not so much one of math as of language, though it does illustrate why so many people hate word problems. It seems that the world has two people: One is a person with good verbal skills and little mathematical acuity; what is the probability the other is someone with good math skills but few lingual ones?