"I have a two children, one of which is a boy. What's the probability the other is a boy?" Intuition wrongly treats the possibilities as sets and assigns proba

"I have a two children, one of which is a boy. What's the probability the other is a boy?" Intuition wrongly treats the possibilities as sets and assigns probabilities 1/2 BB, 1/2 GB, rather than 1/3 BB, 1/3 GB, 1/3 BG.