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(C) Let the sample space for two children be $S = \{BB, BG, GB, GG\}$,where $B$ denotes a boy and $G$ denotes a girl. Each outcome is equally likely w

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$1/3$

Vedclass · Answer

(C) Let the sample space for two children be $S = \{BB, BG, GB, GG\}$,where $B$ denotes a boy and $G$ denotes a girl. Each outcome is equally likely with probability $1/4$.Let $A$ be the event that at least one child is a boy. Then $A = \{BB, BG, GB\}$,so $P(A) = 3/4$.Let $B$ be the event that both children are boys. Then $B = \{BB\}$.We want to find the conditional probability $P(B|A)$,which is the probability that both are boys given that at least one is a boy.$P(B|A) = \frac{P(B \cap A)}{P(A)}$.Since $B \subset A$,$B \cap A = B = \{BB\}$,so $P(B \cap A) = 1/4$.Therefore,$P(B|A) = \frac{1/4}{3/4} = 1/3$.

$A$ parent has two children. If at least one of them is a boy,then the probability that the other is also a boy is:

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