This is an old revision of the document!
What is the probability of the other child being a girl?
Wikipedia: Boy or girl paradox
Reddit: I don't get it
Youtube: Internet baffled by probability riddle
This is what inspired me to stick with it: Youtube: Feynman inspiration
Let P be the probability of at least one of two children being a girl.
Mary has two children, if that is all you know, these families are equally probable: BB BG GB GG
Thus P = 3/4.
If Mary tells you she has at least one boy, these are equally likely: BB BG GB P = 2/3.
If Mary tells you her first child is boy, these are equally likely: BB BG P is 1/2.
If Mary doesn't say anything, but you see Mary walking with one of her children, chosen at random, her family must be one of: BB BG GB But the probability of choosing a B to walk with is TWICE if BB. BB BG GB are not equally probable, BB is twice as probable, if all you observe is the walk. P =1/2.
But if Mary told you, prior to you observing the walk, that she has at least one boy, P=2/3. What if you subsequently observe a walk with a girl? P =1
What if you subsequently observe her walking a boy? P=1/2 or P =2/3? I say P=1/2.
If Mary makes a statement about one of her children, _chosen_ _at_ _random_, and the statement reveals the gender, and the child is a boy, I say P=1/2.