Mathematics
The following table shows the relationship between the monthly incomes and the number of vehicles in a family. If 2000 families, in a locality, are selected, the information gathered is listed in the table below :
| Monthly income (₹) | 0 vehicle | 1 vehicle | 2 or more than 2 vehicles |
|---|---|---|---|
| Less than 10,000 | 1 | 140 | 13 |
| 10,000 - 12,000 | 2 | 285 | 17 |
| 12,000 - 14,000 | 0 | 515 | 0 |
| 14,000 - 16,000 | 0 | 449 | 9 |
| 16,000 or more | 3 | 559 | 7 |
A family is chosen, write the probability that the family chosen is :
(i) earning ₹ 10,000 - ₹ 12,000 per month and owning exactly 1 (one) vehicle.
(ii) earning ₹ 14,000 or more per month and owning 2 or more than 2 vehicles.
(iii) not owning more than 1 vehicle.
Probability
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Answer
Total number of families = 2000.
By formula,
Probability of an event =
(i) Number of families earning ₹ 10,000 - ₹ 12,000 per month and owning exactly 1 vehicle = 285.
∴ Required probability = .
Hence, the required probability = .
(ii) Number of families earning ₹ 14,000 or more per month and owning 2 or more vehicles = 9 + 7 = 16.
∴ Required probability = .
Hence, the required probability = .
(iii) Families not owning more than 1 vehicle are those owning 0 or 1 vehicle.
Number of such families = (1 + 2 + 0 + 0 + 3) + (140 + 285 + 515 + 449 + 559)
= 6 + 1948 = 1954.
∴ Required probability = .
Hence, the required probability = .
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