Question

1000 families with 2 children were selected randomly, and the following data was recorded:
$\begin{array}{cccc}\text{Number of girls in a family}& 2& 1& 0\\ \text{Number of families}& 400& 350& 250\end{array}$

Compute the probability of a family, chosen at random, having
(i) 2 girls.
(ii) 1 girl.
(iii) no girl.

Answer 1

Total number of families = 400 + 350 + 250 = 1000

(i) Number of families having 2 girls = 400
$P_1\left(\text{a randomly chosen family has 2 girls}\right)=\frac{\text{Number of families having 2 girls}}{\text{Total number of families}}$
$P_1\left(\text{a randomly chosen family has 2 girls}\right)=\frac{400}{1000}=\frac{4}{10}$

(ii) Number of families having 1 girl = 350
$P_2\left(\text{a randomly chosen family has 1 girl}\right)=\frac{\text{Number of families having 1 girl}}{\text{Total number of families}}$
$P_2\left(\text{a randomly chosen family has 1 girl}\right)=\frac{350}{1000}=\frac{7}{20}$

(iii) Number of families having no girl = 250
$P_3\left(\text{a randomly chosen family has no girl}\right)=\frac{\text{Number of families having no girl}}{\text{Total number of families}}$
$P_3\left(\text{a randomly chosen family has no girl}\right)=\frac{250}{1000}=\frac{1}{4}$