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.
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.