Exercise 2.29

Let $G_i$ be the event that the $i$-th child is a girl. Let $C_i$ be the event that the $i$-th child has property $C$.

$P(G_1\cap G_2|(G_1\cap C_1)\cup (G_2\cap C_2))=\frac{0.25(2p-p^2)}{0.5p+0.5p-0.25p^2}=\frac{0.5(2-p)}{2-0.5p}=\frac{2-p}{4-p}.$

This result confirms the idea that the more rare characteristic $C$ is, the closer we get to specifying which child we mean when we say that at least one of the children has $C$.