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 | 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 Rs10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning Rs16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than Rs7000 per month and does not own any vehicle.
(iv) earning Rs13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.
Total numbers of families = 2400
(i) Numbers of families earning Rs10000 –13000 per month and owning exactly 2 vehicles = 29
Required probability = 29/2400
(ii) Number of families earning Rs16000 or more per month and owning exactly 1 vehicle = 579
Required probability = 579/2400
(iii) Number of families earning less than Rs7000 per month and does not own any vehicle = 10 Required probability = 10/2400 = 1/240
(iv) Number of families earning Rs13000-16000 per month and owning more than 2 vehicles = 25
Required probability = 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
Required probability = 2062/2400 = 1031/1200
