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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

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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.

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Total numbers of families = 1500

(i) Numbers of families having 2 girls = 475

Probability = Numbers of families having 2 girls/Total numbers of families

= \(\frac{475}{1500}\)

= \(\frac{19}{60}\)

(ii) Numbers of families having 1 girls = 814

Probability = Numbers of families having 1 girls/Total numbers of families

= \(\frac{814}{1500}\)

= \(\frac{407}{750}\)

(iii) Numbers of families having 2 girls = 211

Probability = Numbers of families having 0 girls/Total numbers of families

= \(\frac{211}{1500}\)

Sum of the probability = \(\frac{19}{60}\) + \(\frac{407}{750}\) + \(\frac{211}{1500}\)

= \(\frac{475 + 814 + 211}{1500}\)

= \(\frac{1500}{1500}\) = 1

Yes, the sum of these probabilities is 1.

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