Question

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 (₹)	Number of vehicles per family
	0	1	2 or more than 1
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:

1. earning ₹ 10,000 - ₹ 12,000 per month and owning exactly 1 (one) vehicle.
2. earning ₹ 14,000 or more per month and owning 2 or more than 2 vehicles.
3. not owning more than 1 vehicle.

Answer 1

Total number of families = 2000.

By formula,

Probability of an event = \[\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\]

i. Number of families earning ₹ 10,000 - ₹ 12,000 per month and owning exactly 1 vehicle = 285.

∴ Required probability = \[\frac{285}{2000} = \frac{57}{400}\]

Hence, the required probability = \[\frac{57}{400}\]

ii. Number of families earning ₹ 14,000 or more per month and owning 2 or more vehicles = \[9 + 7 = 16\]

∴ Required probability = \[\frac{16}{2000} = \frac{1}{125}\]

Hence, the required probability = \[\frac{1}{125}\]

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 = \[\frac{1954}{2000} = \frac{977}{1000}\]

Hence, the required probability = \[\frac{977}{1000}\]