Question

$X$ has three children in his family. The probability of one girl and two boys is......

• A. $\frac{1}{8}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{3}{8}$

Answer 1

Answer: (D)

$\frac{3}{8}$

$X$ has $3$ children in his family.

All possible outcomes are if G represents girl child and $B$ represent boy child,$\left\{\right(BBB),(BBG),(BGB),(BGG),(GBB),(GBG),(GGB),(GGG\left)\right\}$, hence $n\left(S\right)=8$

Out of which favorable outcomes for one girl and two boys are, $n\left(E\right)=3$

Hence, the probability that there are one girl and two boys is $\frac{n\left(E\right)}{n\left(S\right)}=\frac{3}{8}$