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 |
Vehicles per family |
|||
(in र) |
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 र 10000–13000 per month and owning exactly 2 vehicles.
(ii) earning र 16000 or more per month and owning exactly l vehicle.
(iii) earning less than र 7000 per month and does not own any vehicle.
(iv) earning र 13000–16000 per month and owning more than 2 vehicles.
(v) owning not more than I vehicle.
Total number of families selected = 2400
(i) Number of families earning र10000–13000 per month and owning exactly 2 vehicles = 29
∴ Probability that the family chosen is earning र10000–13000 per month and owning
exactly 2 vehicles =
(ii) Number of families earning र16000 or more per month and owning exactly 1 vehicle = 579
∴ Probability that the family chosen is earning र16000 or more per month and owning
exactly 1 vehicle =
(iii) Number of families earning less than र 7000 per month and does not own any vehicle =10
Probability that the family chosen is earning less than र7000 per month and does not own any vehicle =
(iv) Number of families earning र13000–16000 per month and owning more than 2 vehicles = 25
∴ Probability that the family chosen is earning र13000–16000 per month and owning
more than 2 vehicles =
(v) Number of families owning not more than 1 vehicle
= Number of families owning 0 vehicle + Number of families owning 1 vehicle = (10 + 0+ 1 + 2 + 1) +(160 + 305 + 535 + 469 +579) = 14 + 2048 = 2062
∴ Probability that the family chosen owns not more than 1 vehicle =