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: Vehicles per family → Monthly income (Rs.) 0 1 2 Above 2 Less than 7,000 10 160 25 0 7,000 - 10,000 0 305 27 2 10,000 - 13,000 1 535 29 1 13,000 - 16,000 2 469 59 25 16,000 or more 1 579 82 88 Suppose a family is chosen. Find the probability that the family chosen is (i) earning Rs. 10,000-13,000 per month and owning exactly 2 vehicles. (ii) earning Rs. 16,000 or more per month and owning exactly 1 vehicle. (iii) earning less than Rs. 7,000 per month and does not own any vehicle. (iv) earning Rs. 13,000-16,000 per month and owning more than 2 vehicles. (v) owning not more than 1 vehicle.

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:

Vehicles per family → Monthly income (Rs.)
0 1 2 Above 2
Less than 7,000 10 160 25 0
7,000 - 10,000 0 305 27 2
10,000 - 13,000 1 535 29 1
13,000 - 16,000 2 469 59 25
16,000 or more 1 579 82 88

Suppose a family is chosen. Find the probability that the family chosen is
(i) earning Rs. 10,000-13,000 per month and owning exactly 2 vehicles.
(ii) earning Rs. 16,000 or more per month and owning exactly 1 vehicle.
(iii) earning less than Rs. 7,000 per month and does not own any vehicle.
(iv) earning Rs. 13,000-16,000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.

Solution:

Number of families surveyed = 10 + 160 + 25 + 0 + 0 + 305 + 27 + 2 + 1 + 535 + 29 + 1 + 2 + 469 + 59 + 25 + 579 + 82 + 88 = 2400

(i) Number of families earning Rs. 10,000-13,000 per month and owning exactly 2 vehicles = 29
P = 29/2400

(ii) Number of families earning Rs. 16,000 or more per month and owning exactly 1 vehicle = 579
P = 579/2400

(iii) Number of families earning less than Rs. 7,000 per month and does not own any vehicle = 10
P = 10/2400 = 1/240

(iv) Number of families earning Rs. 13,000-16,000 per month and owning more than 2 vehicles = 25
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
P = 2062/2400 = 1031/1200

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