Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?

Question

$\begin{array}{1 1} \text{P (youngest is a girl) = 1/2, P (at least one is a girl) = 1/3 }\\\text{P (youngest is a girl) = 1/3, P (at least one is a girl) = 1/2} \\\text{P (youngest is a girl) = 1/3, P (at least one is a girl) = 1/4} \\ \text{P (youngest is a girl) = 1/2, P (at least one is a girl) = 2/3} \end{array}$