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:
Monthly income (in Rs) | Vehicles per family | |||
0 | 1 | 2 | Above 2 | |
Less than 7000 7000 – 10000 10000 – 13000 13000 – 16000 16000 or more | 10 0 1 2 1 | 160 305 535 469 579 | 25 27 29 59 82 | 0 2 1 25 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
Total number of families = 2400
(i) Number of families earning Rs. 10,000 – 13,000 per month and owning exactly two vehicles = 29
Hence,
Probability of families earning Rs. 10,000 – 13,000 per month and owning exactly two vehicles will be,
(ii) Number of families earning Rs. 16000 or more per month and owning exactly one vehicle = 579
Hence,
Probability of families earning Rs. 16000 or more per month and owning exactly one vehicle will be,
(iii) Number of families earning less than Rs. 7000 per month and does not own any vehicle = 10
Hence,
Probability of families earning less than Rs. 7,000 per month and doesn’t own any vehicles will be,
(iv) Number of families earning Rs. 13,000-16000 per month and owning more than two vehicles = 25
Hence,
Probability of families earning Rs. 13,000-16000 per month and owning more than two vehicles will be,
(v) Number of families owning not more than 1 vehicle are
= 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1 + 579
= 2062
Hence,
Probability of families owning not more than one vehicle will be
