Assume that each born child is equally likely | vedclass

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(C) Let $b$ and $g$ represent the boy and girl child respectively. If a family has two children,the sample space is $S = \{(b, b), (b, g), (g, b), (g,

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$1/2$

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(C) Let $b$ and $g$ represent the boy and girl child respectively. If a family has two children,the sample space is $S = \{(b, b), (b, g), (g, b), (g, g)\}$.Let $A$ be the event that both children are girls. Thus,$A = \{(g, g)\}$.Let $B$ be the event that the youngest child is a girl. Thus,$B = \{(b, g), (g, g)\}$.The intersection is $A \cap B = \{(g, g)\}$.The probability of event $B$ is $P(B) = \frac{2}{4} = \frac{1}{2}$.The probability of the intersection is $P(A \cap B) = \frac{1}{4}$.The conditional probability that both are girls given that the youngest child is a girl is $P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{1/4}{1/2} = \frac{1}{2}$.

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 the youngest is a girl?

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