 # 1500 families with 2 children were selected randomly, and the following data were recorded: 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.

 Number of girls in a family 2 1 0 Number of families 475 814 211

Solution

According to the given parameters
Total numbers of families given in the question 1500
(i) 2 girls

Numbers of families having 2 girls = 475
Probability of choosen 2 girls = Numbers of families having 2 girls / Total numbers of families
= 475/1500 = 19/60
Probability of choosen 2 girls is 19/60

(ii) 1 girl

Numbers of families having 1 girls = 814
Probability of chosen 1 girl = Numbers of families having 1 girl / Total numbers of families
= 814/1500 = 407/750
The probability of chosen 1 girl is 407/750

(iii) No girl

(iii) Numbers of families having 0 girls = 211
Probability of choosen 0 girl = Numbers of families having 0 girls/Total numbers of families
= 211/1500

Sum of the probability = (19/60)+(407/750)+(211/1500)
= (475+814+211)/1500
= 1500/1500 = 1

Yes, the sum of these probabilities is 1.