Question

A couple has $2$ children. The probability that both are boys, if it is known that at least one of the children is a boy is

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

Answer: (B)

$\frac{1}{3}$

Let $B$ stand for Boys and $G$ for girls.
Then possibility of two children will of the following types
$BB,BG,GB,GG$.
Now it is given that atleast $1$ is a boy.
Hence total number of possibilities
$=[BB,BG,GB,GG]-GG$
$=BB,BG,GB$
$=3$.
Now in the sample set there is only $1$ element where both the children are Boys.
Hence the required probability is
$=\frac{1}{3}$