B/G
B/B
Is it 50%?
no. once again, like in the monty hall question, its helpful to exaggerate the problem and add more variables.
what if there were 100 kids and i was told at least one is a boy. would there still be a 50% chance of EVERY kid being a boy? hell no.
same thing applies here. the 2nd kid changes the simple B/B, B/G options. since there is another kid, there are three possibilities now:
Kid 1= Boy, Kid 2= Girl
Kid 1= Girl, Kid 2=Boy
Both Kids Boys
so three options, one good option, thus 1/3 chance.
another way of looking at it. suppose that we didnt know that one of the kids was a boy, then there would be a 25% chance of a Boy/Boy combo right? well lets look closer at our options:
Kid 1= Girl, Kid 2= Girl
Kid 1= Boy, Kid 2= Girl
Kid 1= Girl, Kid 2=Boy
Both Kids Boys
look, there are two B/G options. why would one of them be omitted if we are told one kid is a boy? the only thing that is lost is the G/G option.
one of the most important features of the puzzle is the "we dont know any more information about the kids" part. if we knew the younger kid was a boy, then yes, it would be a 50% chance of being B/B.