Question

An organisation selected 2400 families at random and surveyed them to determine a relationship between the income level and the number of vehicles in a family. The information gathered is listed in the table below:

Suppose a family is chosen at random. Find the probability that the family chosen is

(i) earning Rs 25000 - Rs 30000 per month and owning exactly 2 vehicles.

(ii) earning Rs 40000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 25000 per month and not owning any vehicle.

(iv) earning Rs 35000 - Rs 40000 per month and owning 2 or more vehicles.

(v) owning not more than 1 vehicle.

Answer 1

ANSWER:
Number of families surveyed = 2400
(i) Number of families earning ₹ 25000 – ₹ 30000 per month and owning exactly 2 vehicles = 27
∴ P(Family chosen is earning ₹ 25000 – ₹ 30000 per month and owning exactly 2 vehicles)
$=\frac{\text{Number of families earning ₹ 25000 – ₹ 30000 per month and owning exactly 2 vehicles}}{\text{Number of families surveyed}}$
$=\frac{27}{2400}=\frac{9}{800}$
(ii) Number of families earning ₹ 40000 or more per month and owning exactly 1 vehicle = 579
∴ P(Family chosen is earning ₹ 40000 or more per month and owning exactly 1 vehicle)
=$\frac{\text{Number of families earning ₹ 40000 or more per month and owning exactly 1 vehicle}}{\text{Number of families surveyed}}$
=$\frac{579}{2400}=\frac{193}{800}$
(iii) Number of families earning less than ₹ 25000 per month and not owning any vehicle = 10
∴ P(Family chosen is earning less than ₹ 25000 per month and not owning any vehicle)=$\frac{\text{Number of families earning less than ₹ 25000 per month and not owning any vehicle}}{\text{Number of families surveyed}}$
$=\frac{10}{2400}=\frac{1}{240}$
(iv) Number of families earning ₹ 35000 – ₹ 40000 per month and owning 2 or more vehicles = 59 + 25 = 84
∴ P(Family chosen is earning ₹ 35000 – ₹ 40000 per month and owning 2 or more vehicles)
=$\frac{\text{Number of families earning ₹ 35000 – ₹ 40000 per month and owning 2 or more vehicles}}{\text{Number of families surveyed}}=\frac{84}{2400}=\frac{7}{200}$
(v) Number of families owning not more than 1 vehicle
= Number of families owning 0 vehicles + Number of families owning 1 vehicle
= 10 + 0 + 1 + 2 + 1 + 160 + 305 + 535 + 469 + 579 = 2062
∴ P(Family chosen is owning not more than 1 vehicle)
= $\frac{\text{Number of families owning not more than 1 vehicle}}{\text{Number of families surveyed}}$
=$\frac{2062}{2400}=\frac{1031}{1200}$