An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:

Suppose a family is chosen. Find the probability that the family chosen is
(i) earning ₹ 10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning ₹ 16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than ₹ 7000 per month and does not own any vehicle.
(iv) earning ₹ 13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.

Solution:

The probability of a certain event is given by the ratio of a particular occurrence of an event by the total number of events.

Probability of having vehicle-based on the earnings = Number of vehicles per family based on earnings/Total number of families

Total number of families = 2400

• A family earning ₹10000 – 13000 per month and owning exactly 2 vehicles = 29
• Family earning ₹16000 or more per month and owning exactly 1 vehicle = 579
• Family earning less than ₹7000 per month and does not own any vehicle = 10
• Family earning ₹13000 – 16000 per month and owning more than 2 vehicles = 25
• Family owning not more than 1 vehicle = 10 + 0 + 1 + 2 + 1 + 160 + 305 + 535 + 469 + 579 = 2062

(i) Probability of family earning ₹ 10000 – 13000 per month and owning exactly 2 vehicles = 29/2400

(ii) Probability of family earning ₹ 16000 or more per month and owning exactly 1 vehicle = 579/2400

(iii) Probability of family earning less than ₹ 7000 per month and does not own any vehicle = 10/2400 = 1/240

(iv) Probability of family earning ₹ 13000 – 16000 per month and owning more than 2 vehicles = 25/2400 = 1/96

(v) Probability of family owning not more than 1 vehicle = 2062/2400 = 1031/1200

☛ Check: NCERT Solutions for Class 9 Maths Chapter 15

Video Solution:

An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:

NCERT Solutions for Class 9 Maths Chapter 15 Exercise 15.1 Question 5

Summary:

The probability of family earning ₹ 10000 – 13000 per month and owning exactly 2 vehicles = 29/2400, probability of family earning ₹ 16000 or more per month and owning exactly 1 vehicle = 579/2400, probability of family earning less than ₹ 7000 per month and does not own any vehicle = 10/2400 = 1/240, probability of family earning ₹ 13000 – 16000 per month and owning more than 2 vehicles = 25/2400 = 1/96, probability of family owning not more than 1 vehicle = 2062/2400 = 1031/1200.

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