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

(0 2 girls (ii) 1 girl (iii) No girl.

Also check whether the sum of these probabilities is 1.

Solution

Total number of families
= 475 + 814 + 211 = 1500
(i) Probability of a family, chosen at random,
having 2 girls = $475 over 1500 equals 19 over 60$
(ii) Probability of a family, chosen at random,
having 1 girl $equals 814 over 1500 equals 407 over 750$
(iii) Probability of a family, chosen at random,
having no girl $equals 211 over 1500$
Sum of these probabilities
$equals 19 over 60 plus 407 over 750 plus 211 over 1500 equals fraction numerator 475 plus 814 plus 211 over denominator 1500 end fraction equals 1500 over 1500 equals 1$
Hence, the sum is checked.