Let me try another scenario. A woman says, "I have two children." You respond, "What are their sexes?" She says, "At least one of them is a boy. The other was kidnapped before I was informed of its sex." You're saying that the chance that the kidnapped child is a boy is one out of three, not out of two? To repeat: That's what I gather from the present post, near the beginning of which is the following:

In the correct version of this story, the mathematician says "I have two children", and you ask, "Is at least one a boy?", and she answers "Yes". Then the probability is 1/3 that they are both boys.

Having no training in probability, and having come upon the present website less than a day ago, I'm hoping someone here will be able to explain to me something basic. Let's assume, as is apparently assumed in this post, a 50-50 boy-girl chance. In other words, the chance is one out of two that a child will be a boy -- or that it will be a girl. A woman says, "I have two children." You respond, "Boys or girls?" She says, "Well, at least one of them is a boy. I haven't yet been informed of the sex of the other, to whom I've just given birth." You're saying that the chance that the newborn is a boy is one out of three, not one out of two? That's what I gather from the present post, near the beginning of which is the following:

In the correct version of this story, the mathematician says "I have two children", and you ask, "Is at least one a boy?", and she answers "Yes". Then the probability is 1/3 that they are both boys.