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 weather the sum of these probabilities is 1.

Total number of family = 475 + 814 + 211 = 1500

i) number of families of 2 girls = 475

So, we get that,

P1 =\( \frac{Number of families having 2 girls}{Total number of family}\)
p =\( \frac{475}{1500} = \frac{19}{60}\).

Therefore, the probability of a family, chosen at random, is having 2 girls

ii) Number of families having 1 girl = 814

So, we get that,

P2 = \( \frac{Number of families having 1 girls}{Total number of family}\)
p = \(\frac{814}{1500} = \frac{407}{750}\)..

Therefore, the probability of a family, chosen at random, is having 2 girls

iii) Number of families having no girl = 211
So, we get that,

\(P3 = \frac{Number of families having 0 girls}{Total number of family}\)
\(p = \frac{211}{1500}\).

Therefore, the probability of a family, chosen at random, is having 2 girls

Now, Sum of all these probabilities
= P1 + P2 + P3
= \(\frac{19}{60} + \frac{407}{750} + \frac{211}{1500}\)
\(= \frac{475 + 814 + 211}{1500}\)
\(= \frac{1500}{1500} = 1\)

Hence, we can say that,
The sum of these probabilities is 1.