The question is ill posed, because the anwser is highly dependent on how the couple told you that they have one girl. If they tell you "we have two kids", you

The question is ill posed, because the anwser is highly dependent on how the couple told you that they have one girl. If they tell you "we have two kids", you ask them if at least one of them is a girl and they answer "yes", then indeed the probability of the other kid beeing a boy is 2/3. If they tell you "we have two kids, and one of them is a girl", then by all rules of rational discourse the probability for the other kid being a boy is 1. Things start to get interesting if the talking member of the couple is a mathematician (so the rules of ordinary discourse do not apply) and he says "We have two kids, and at least one of them is a girl". Now you might say that this is equivalent two the first case. But you could also go bayesian and look at the possible conversations with couples containing at least one mathematician that have two kids. Say you have 100 couples. On average, 25 of these will have two boys and tell you "We have two kids, and at least one of them is a boy", another 25 will have two girls and tell you "We have two kids, and at least one of them is a girl". The remaining 50 couples will have one boy and one girl. Assuming no gender bias on behalf of the speaking mathematician (ha!), 25 of these will tell you "We have two kids, and at least one of them is a boy", while the remaining 25 will say "We have two kids, and at least one of them is a girl." So out of the 50 couples that tell you "We have two kids, and at least one of them is a girl," 25 will have two girls, and 25 will have a boy and a girl. So in this case, the correct answer is 1/2. (This is essentially the argument from the intro on this page that was linked from the discussion on coding horror: http://www.overcomingbias.com/2008/10/my-bayesian-enl.html http://www.overcomingbias.com/2008/10/my-bayesian-enl.html )