1500 families with two children are selected randomly according to the data given below.
Number of girls in a family | 0 | 1 | 2 |
Number of families | 211 | 814 | 475 |
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.
Mathematics
Bsc
1897
Valentina
Here, Total number of families = 1500
(i) Number of families having 2 girls = 475, therefore, Probability of selecting a family having 2 girls equals = 475 / 1500 = 19 / 60
(ii) Number of families having 1 girl = 814, therefore, Probability of selecting a family having 1 girl = 814 / 1500 = 407 / 750
(iii) Number of families having no girl = 211, therefore, Probability of selecting a family having no girl = 211 / 1500.
Now, the sum of the obtained probabilities are = 19/60 + 407/750 + 211/1500
= (475 + 814 + 211)1500 = 1500/1500 = 1
i.e., Sum of the above probabilities is equal to 1.
Given that the total number of families is 1500
When we add all the three probabilities: 475/60 + 814/750 + 211/1500 = 1500/1500 = 1. Therefore, the sum of the above probabilities is equal to 1 which is equal to 100%.