Question :

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

##### Views

2106

Valentina

Knowledge

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.

Rajiv Sharma

Given that the total number of families is 1500

1. According to the given table, families having 2 girls is 475. Therefore, the probability of having 2 girls in a family = 475 / 1500 = 19 / 60
2. According to the given table, families having 1 girl is 814. Therefore, the probability of having 1 girl in a family = 814 / 1500 = 407 / 750
3. According to the given table, families having no girl = 211. Therefore, the probability of having no girl in a family = 211 / 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%.

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