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Introduction To Mathematical Modelling

Question

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

Number of girls in a family

2

1

0

Number of families

475

814

211

Compute the probability of a family, chosen at random, having

(0 2 girls (ii) 1 girl (iii) No girl.

Also check whether the sum of these probabilities is 1.

Solution

Total number of families
= 475 + 814 + 211 = 1500
(i) Probability of a family, chosen at random,
having 2 girls = $475 over 1500 equals 19 over 60$
(ii) Probability of a family, chosen at random,
having 1 girl $equals 814 over 1500 equals 407 over 750$
(iii) Probability of a family, chosen at random,
having no girl $equals 211 over 1500$
Sum of these probabilities
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Hence, the sum is checked.

Some More Questions From Introduction to Mathematical Modelling Chapter

Activity: Note the frequency of two wheelers, three wheelers and four wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Activity: Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3 ? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

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