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(B) Let $b$ represent a boy and $g$ represent a girl. For a family with two children,the sample space $S$ is given by: $S = \{(b, b), (b, g), (g, b),

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$1/3$

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(B) Let $b$ represent a boy and $g$ represent a girl. For a family with two children,the sample space $S$ is given by: $S = \{(b, b), (b, g), (g, b), (g, g)\}$ Let $A$ be the event that both children are girls: $A = \{(g, g)\}$ Let $C$ be the event that at least one child is a girl: $C = \{(b, g), (g, b), (g, g)\}$ Then,the intersection $A \cap C$ is: $A \cap C = \{(g, g)\}$ The probability of event $C$ is $P(C) = \frac{3}{4}$. The probability of the intersection is $P(A \cap C) = \frac{1}{4}$. The conditional probability $P(A|C)$ is calculated as: $P(A|C) = \frac{P(A \cap C)}{P(C)} = \frac{1/4}{3/4} = \frac{1}{3}$.

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 at least one is a girl?

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