Question :

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.

Maths

Class 9

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313

Qayanat

Aanya

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.

Here, total number of families = 2400

(i) Number of families earning Rs. 10000 – Rs. 13000 per month and owning exactly 2 vehicles = 29.

THerefore, Probability of a family earning Rs. 10000 – Rs. 13000 per month and owning exactly 2 vehicles = 29 / 2400

(ii) Number of families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579

Therefore, Probability of a family earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579 / 2400

(iii) Number of families earning less than Rs. 7000 per month and do not own any vehicle = 10

Therefore, Probability of a family earning less than Rs. 7000 per month and does not own any vehicle = 10 / 2400 = 1 / 240

(iv) Number of families earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles = 25

Therefore, Probability of a family earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles = 25 / 2400 = 1 / 96

(v) Number of families owning not more than 1 vehicle = [Number of families having no vehicle] + [Number of families having only 1 vehicle]

= [10 + 1 + 2 + 1] + [160 + 305 + 535 + 469 + 579]

= 14 + 2048 = 2062

Therefore, Probability of a family owning not more than 1 vehicle = 2062 / 2400 = 1031 / 1200

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