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A pair has two children. If one of them is boy, then the probability that other is also a boy, is
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The correct answer is:
$\frac{1}{3}$
Let $P(A)=$ probability of a boy in two children $=\frac{3}{4}$
Because cases are $B B, B G, G B, G G=4$
Favourable cases are $B B, B G, G B=3$
The probability that the second child is also boy is $P(A \cap B)=\frac{1}{4}$
We have to find $P(B / A)=\frac{P(A \cap B)}{P(A)}=\frac{1 / 4}{3 / 4}=\frac{1}{3}$.
Because cases are $B B, B G, G B, G G=4$
Favourable cases are $B B, B G, G B=3$
The probability that the second child is also boy is $P(A \cap B)=\frac{1}{4}$
We have to find $P(B / A)=\frac{P(A \cap B)}{P(A)}=\frac{1 / 4}{3 / 4}=\frac{1}{3}$.
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