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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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