Depends on the nature of the utterance.

If someone asks the question to a person who has two children “Is one of your children a boy?” Then, of the people who answer “Yes, one of my children is a boy”, there is a 1 in 3 chance that the other child is a boy.

If someone asks the question to a person who has two children: “Tell me the gender of one of your children”. Then of the people who answer “One of my children is a boy”, there is a 1 in 2 chance that the other child is a boy.


Detailed argument for each follows.

For the first case, start with 1000 people that two children and ask them the question “Is one of your children a boy”. On average, 250 people will have 2 girls and say “No, none of my children is a boy”. On average 500 people will have a boy and a girl and say “Yes, one of my children is a boy”. On average, 250 people will have 2 boys and say “Yes, one of my children is a boy”.

Thus 750 people will say “Yes, one of my children is a boy” and out of those 750, in 250 cases will the other child be a boy. Thus 1 in 3.

For the second case, start with 1000 people that two children and ask them the question “Tell me the gender of one of your children”. On average, 250 people will have 2 girls and all will say “One of my children is a girl”. On average 500 people will have a boy and a girl and on average 250 of those will say “One of my children is a boy”. On average, 250 people will have 2 boys and all 250 will say “One of my children is a boy”.

Thus on aveage 500 people will say “One of my children is a boy” and out of those 500, in 250 cases will the other child be a boy. Thus 1 in 2.