It's all a question about the correct precodition definition. I think people who heard about conditional probability know that the correct answer is "2/3". Most

It's all a question about the correct precodition definition. I think people who heard about conditional probability know that the correct answer is "2/3". Most people will just imagine the first precondition "they have two children" and forget the second one. What about going in the opposite direction and simply ask "What is the probability that a mother has a boy and a girl?" I think many people would answer "1/2", too, simply adding the precodition "she has 2 children" ;) The origin for this is - I think - an implicit context people are thinking of without real awareness of it. You think quicker with implicit context.