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

Number of girls in a family	$2$	$1$	$0$
Number 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 $1$.

(N/A) Total number of families $= 475 + 814 + 211 = 1500$.
$(i)$ Number of families having $2$ girls $= 475$.
Probability $(P_1)$ of a randomly chosen family having $2$ girls $= \frac{475}{1500} = \frac{19}{60}$.
$(ii)$ Number of families having $1$ girl $= 814$.
Probability $(P_2)$ of a randomly chosen family having $1$ girl $= \frac{814}{1500} = \frac{407}{750}$.
$(iii)$ Number of families having no girl $= 211$.
Probability $(P_3)$ of a randomly chosen family having no girl $= \frac{211}{1500}$.
Sum of all these probabilities $= P_1 + P_2 + P_3 = \frac{475}{1500} + \frac{814}{1500} + \frac{211}{1500} = \frac{475 + 814 + 211}{1500} = \frac{1500}{1500} = 1$.
Therefore,the sum of all these probabilities is $1$.