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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, so P = 2/3.
If Mary tells you her first child is boy, these are equally likely: BB BG, so P is 1/2.
Suppose the culture is that, at a certain hour, mothers flip a coin to choose a child to take out for a walk. You will see half the children are boys, half are girls. You see Mary with a boy. So Mary's 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, obviously.
What if you subsequently observe Mary walking a boy? P=1/2 or P=2/3? I say P=1/2. Mary's prior statement is a corollary of this new observation.
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. But if the culture is that no public statements are allowed about girls, then BB BG and GB are equally probable. I say P=2/3.