Question

$1500$ families with $2$ children were selected randomly, and the following data were recorded:

No. of girls in a family	$2$	$1$	$0$
No. of families	$475$	$814$	$211$

Compute the probability of a family, chosen at random, having
(i) $2$ girls
(ii) $1$ girl
(iii) No girl
Also check whether the sum of these probabilities is $1$.

Answer 1

(i) Number of families having $2$ girls $=475$
Total families $=475+814+211=1500$

$P(2$ girls$)=\frac{475}{\text{Total families}}$

$=\frac{475}{1500}=\frac{19}{60}$

(ii) $P(1$ girl$)=\frac{814}{1500}=\frac{407}{750}$

(iii) $P($No girl$)=\frac{211}{1500}$

Sum of all these probabilities

$=\frac{19}{60}+\frac{407}{750}+\frac{211}{1500}$

$=\frac{475+814+211}{1500}$

$=\frac{1500}{1500}=1$

Sum of these probabilities $=1$