Question

In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?

• A. $\frac{3}{23}$
• B. $\frac{6}{23}$
• C. $\frac{3}{10}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B $\frac{6}{23}$

Number of children belonging to families with 3 children
$=\left(50percentageofN\right)\times 3=\frac{3N}{2}$

Number of children belonging to families with 2 children
$=\left(30percentageofN\right)\times 2=\frac{3N}{5}$

Number of children belonging to families with 1 child
$=\left(20percentageofN\right)\times 1=\frac{N}{5}$

Required probability $=\frac{\frac{3N}{5}}{\frac{3N}{2}+\frac{3N}{5}+\frac{N}{5}}=\frac{6}{23}$