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Question

1500 families with 2 children were selected randomly and the following data were recorded:
Number of girls in a family 0 1 2
Number of families 211 814 475

If a family is chosen at random, compute the probability that it has:
(i) No girl
(ii) 1 girl
(iii) 2 girls
(iv) at most one girl
(v) more girls than boys

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Solution

The total number of trials is 1500.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A be the event of having no girl.

The number of times A happens is 211.

Therefore, we have

(ii) Let B be the event of having one girl.

The number of times B happens is 814.

Therefore, we have

(iii) Let C be the event of having two girls.

The number of times C happens is 475.

Therefore, we have

(iv) Let D be the event of having at most one girl.

The number of times D happens is.

Therefore, we have

(v) Let E be the event of having more girls than boys.

The number of times E happens is 475.

Therefore, we have


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