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.

Solution:

Probability of an event, P(E) = Number of occurrences where the event takes place / Total number of occurrences

The probability of selecting a family having 2 girls, 1 girl, and no girl will be the ratio of the number of girls in the family and the total number of families.

Total number of families = 1500

Number of families having 2 girls = 475

Number of families having 1 girl = 814

Number of families having no girl = 211

(i) Probability of family having 2 girls, P(2) = Family having 2 girls / Total number of families

Therefore, P(2) = 475/1500 = 19/60

(ii) Probability of family having 1 girl, P(1) = Family having 1 girl / Total number of families

Therefore, P(1) = 814/1500 = 407/750

(iii) Probability of family having no girl, P(0) = Family having no girl / Total number of families

Therefore, P(0) = 211/1500

Now, sum of all the three probabilities = P(2) + P(1) + P(0)

= 475/1500 + 814/1500 + 211/1500

= (475 + 814 + 211) / 1500

= 1500/1500

= 1

☛ Check: NCERT Solutions Class 9 Maths Chapter 15

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Video Solution:

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

NCERT Solutions for Class 9 Maths Chapter 15 Exercise 15.1 Question 2

Summary:

It is given that 500 families with 2 children were selected randomly. We found that the probability of a family having 2 girls is equal to 475/1500, the probability of a family having 1 girl is equal to 814/1500, and the probability of having no girl is equal to 211/1500. Also, the sum of all the three probabilities = 1.

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