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Question:

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 whether the sum of these probabilities is 1.

Solution:

(i) Number of families having 2 girls = 475
Total families = 475 + 814 + 211 = 1500
P(2 girls) = 475/1500 = 19/60
(ii) P(1 girl) = 814/1500 = 407/750
(iii) P(No girl) = 211/1500
Sum of all these probabilities = 19/60 + 407/750 + 211/1500 = (475 + 814 + 211)/1500 = 1500/1500 = 1
Sum of these probabilities = 1