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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

Vedclass · Accepted Answer

$1/3$

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 $A = \{BB, BG, GB\}$.Let $B$ be the event that both children are boys. Then $B = \{BB\}$.We are given that at least one child is a boy (event $A$ has occurred),and we need to find the conditional probability that both are boys (event $B$ occurs).The conditional probability is given by $P(B|A) = \frac{P(A \cap B)}{P(A)}$.Here,$A \cap B = \{BB\}$,so $P(A \cap B) = 1/4$.Also,$P(A) = 3/4$.Therefore,$P(B|A) = \frac{1/4}{3/4} = 1/3$.

$A$ couple has two children. One of them is a boy. What is the probability that the other child is also a boy?

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