Question

An organization 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:

Monthly income (in Rs)	Vehicles per family
	0	1	2	Above 2
Less than 7000	10	160	25	0
7000 − 10000	0	305	27	2
10000 − 13000	1	535	29	1
13000 − 16000	2	469	59	25
16000 or more	1	579	82	88

Suppose a family is chosen, find the probability that the family chosen is

(i) earning Rs 10000 − 13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 7000 per month and does not own any vehicle.

(iv) earning Rs 13000 − 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

Answer 1

Number of total families surveyed = 10 + 160 + 25 + 0 + 0 + 305 + 27 + 2 + 1 +

535 + 29 + 1 + 2 + 469 + 59 + 25 + 1 + 579 + 82 + 88 = 2400

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

Hence, required probability, P = 29/2400

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

Hence, required probability, P = 579/2400

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

Hence, required probability, P = 10/2400 = 1/240

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

Hence, required probability, P = 25/2400 = 1/96

(v) Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1 + 579 = 2062

Hence, required probability, P = 2062/2400 = 1031/1200