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 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.

Monthly income (in ₹) 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

Solution

Given

According to the given data

Total number of families = 2400 

(i) earning ₹10000 – 13000 per month and owning exactly 2 vehicles.

The probability that the family chosen is earning ₹10000 – 13000 per month and owning exactly 2 vehicles = 
(Numbers of families earning ₹10000 –13000 per month and owning exactly 2 vehicles) / (Total number of families) 
= 29/2400 

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

Number of families earning ₹16000 or more per month and owning exactly 1 vehicle = 579
The probability that the family chosen is earning ₹16000 or more per month and owning exactly 1 vehicle =
(Number of families earning ₹16000 or more per month and owning exactly 1 vehicle) / (Total number of families)
=579/2400 

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

Number of families earning less than ₹7000 per month and does not own any vehicle = 10
The probability that the family chosen is earning less than ₹7000 per month and does not own any vehicle =
(Number of families earning less than ₹7000 per month and does not own any vehicle)/(Total number of families)
= 10/2400 = 1/240

(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.

Number of families earning ₹13000-16000 per month and owning more than 2 vehicles = 25
The probability that the family chosen is earning ₹13000 – 16000 per month and owning more than 2 vehicles =
(Number of families earning ₹13000-16000 per month and owning more than 2 vehicles ) / (Total number of families)
= 25/2400 = 1/96

(v) owning not more than 1 vehicle.

Number of families owning not more than 1 vehicle = 10+160+0+305+1+535+2+469+1+579 = 2062 
The probability that the family chosen owns not more than 1 vehicle = 2062/2400 = 1031/1200

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