If the FIRST round is black, only two of the four possibilities are left, one of which leads to red. Similarly, if Atwood's problem stated that the FIRST child

If the FIRST round is black, only two of the four possibilities are left, one of which leads to red. Similarly, if Atwood's problem stated that the FIRST child is a girl then the probability that the second is a boy is 1/2. The problem, however, states that one of the children is a girl -- it could be the first or the second. In this case the probability that the other child is a boy is 2/3.