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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
Mary has two children, if that is all you know, these families are equally probable: BB BG GB GG
The probability of having at least one girl is 3/4.
If Mary tells you she has at least one boy, these are equally likely: BB BG GB The probability of having at least one girl is 2/3.
If Mary tells you her first child is boy, these are equally likely: BB BG The probability of having at least one girl 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. The probability of having at least on girl is 1/2.
But is Mary tells you that she has at least one boy, that could happen if she is walking either a girl or boy. That is more information than simply observing one child she is walking with.