A couple has two children. Find the probabili | vedclass

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(B) Let $b$ denote a boy and $g$ denote a girl. The sample space for two children is $S = \{(b, b), (b, g), (g, b), (g, g)\}$.Let $E$ be the event tha

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$1/3$

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(B) Let $b$ denote a boy and $g$ denote a girl. The sample space for two children is $S = \{(b, b), (b, g), (g, b), (g, g)\}$.Let $E$ be the event that both children are males,so $E = \{(b, b)\}$.Let $F$ be the event that at least one child is a male,so $F = \{(b, b), (b, g), (g, b)\}$.We need to find the conditional probability $P(E|F)$.The intersection of $E$ and $F$ is $E \cap F = \{(b, b)\}$.The number of elements in $E \cap F$ is $n(E \cap F) = 1$,and the number of elements in $F$ is $n(F) = 3$.Therefore,the probability is $P(E|F) = \frac{n(E \cap F)}{n(F)} = \frac{1}{3}$.

$A$ couple has two children. Find the probability that both children are males,if it is known that at least one of the children is male.

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