Assume that each born child is equally likely to be a boy or a girl. If two families have two childr

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14.Probability

hard

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is

$\frac{1}{10}$

$\frac{1}{17}$

$\frac{1}{12}$

$\frac{1}{11}$

(JEE MAIN-2019)

Solution

$P(B o y)=P(g i r l)=\frac{1}{2}$

Required probability $=\frac{\text { all four girls }}{\text { Atleast two girls }}$

$=\frac{\left(\frac{1}{2}\right)^{4}}{\left(\frac{1}{2}\right)^{4}+^{4} \mathrm{C}_{3}\left(\frac{1}{2}\right)^{4}+^{4} \mathrm{C}_{2}\left(\frac{1}{2}\right)^{4}}$

$=\frac{1}{11}$

Standard 11

Mathematics

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medium

(JEE MAIN-2025)

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