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# 1500 families with 2 children were selected randomly, and the following data were recorded:No. of girls in a family210No. of families475814211Compute the probability of a family,chosen at random, havingi) 2 girlsii) 1 girliii) no girlAlso 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.