problem 29

2.1.22 problem 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 $C$ .

$P (G_{1} \cap G_{2} ∣ ∣ ∣ (G_{1} \cap C_{1}) \cup (G_{2} \cap C_{2})) = \frac{0.25 (2 p - p^{2})}{0.5 p + 0.5 p - 0.25 p^{2}} = \frac{0.5 (2 - p)}{2 - 0.5 p} = \frac{2 - p}{4 - p} .$

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 $C$ .

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