A couple has two children. Find the probabili | vedclass

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(B) Let the sample space $S$ for two children be $\{(b, b), (b, g), (g, b), (g, g)\}$,where $b$ denotes a boy and $g$ denotes a girl.Let $A$ be the ev

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$1/2$

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(B) Let the sample space $S$ for two children be $\{(b, b), (b, g), (g, b), (g, g)\}$,where $b$ denotes a boy and $g$ denotes a girl.Let $A$ be the event that both children are females,so $A = \{(g, g)\}$.Let $B$ be the event that the elder child is a female,so $B = \{(g, b), (g, g)\}$.We need to find the conditional probability $P(A|B)$.The intersection $A \cap B = \{(g, g)\}$.The probability $P(B) = \frac{2}{4} = \frac{1}{2}$.The probability $P(A \cap B) = \frac{1}{4}$.Using the formula for conditional probability,$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{1/4}{1/2} = \frac{1}{2}$.

$A$ couple has two children. Find the probability that both children are females,if it is known that the elder child is a female.

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