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(C) Let $B$ denote a boy and $G$ denote a girl. The possible outcomes for $2$ children are $\{BB, BG, GB, GG\}$,where each outcome is equally likely w

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(C) Let $B$ denote a boy and $G$ denote a girl. The possible outcomes for $2$ children are $\{BB, BG, GB, GG\}$,where each outcome is equally likely with probability $1/4$. Given that at least $1$ child is a boy,the sample space reduces to $S = \{BB, BG, GB\}$. The total number of outcomes in the reduced sample space is $n(S) = 3$. We want to find the probability that the other child is a girl,which corresponds to the outcomes where there is exactly $1$ boy and $1$ girl. These outcomes are $\{BG, GB\}$. The number of favourable outcomes is $n(E) = 2$. Therefore,the required probability is $P(E) = \frac{n(E)}{n(S)} = \frac{2}{3}$.

Ram is visiting a friend. Ram knows that his friend has $2$ children and $1$ of them is a boy. Assuming that a child is equally likely to be a boy or a girl,then the probability that the other child is a girl,is

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