Question

1500 families with 2 chidren were selected randomly and the following data were recorded :

\(\begin{array}{|c|c|c|c|}\hline

\text{Number of girls in a family} & 0 & 1 & 2\\\hline

\text{Number of families} & 211 & 814 & 475 \\\hline

\end{array}\)

If a family is chosen at reandam, copute4 the probability that it has :

(i) No girl (ii) I girl (iii) 2 girls (iv) at most one girl (v) more girls then boys [NCERT]

Answer 1

Total number of families (n) = 1500

\(\begin{array}{|c|c|c|c|}\hline

\text{Number of girls in a family} & 0 & 1 & 2\\\hline

\text{Number of families} & 211 & 814 & 475 \\\hline

\end{array}\)

(i) Probability of a family having no girls (m) 211

$\therefore$ P(A) $\frac{m}{n}=\frac{211}{1500}=0.1406$

(ii) Probability of a family having one girl (m)=814

$\therefore$ P(A) $\frac{m}{n}=\frac{814}{1500}=0.5426$

(iii) Probability of a family having 2 girls (m) =475

$\therefore$ P(A) $\frac{m}{n}=\frac{475}{1500}=0.3166$

(iv) Probability ofa a family having at the most one girls

$\therefore$ m= 814+211=1025

$\therefore$ P(A) $\frac{m}{n}=\frac{1025}{1500}=0.6833$

(v) Probability of a family having more girls than boys (m) =475

$\therefore$ P(A) $\frac{m}{n}=\frac{475}{1500}=0.3166$