Question

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:

Suppose a family is chosen. Find the probability that the family has chosen is

(i) earning ₹10000 – 13000 per month and owning exactly 2 vehicles.

(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than ₹7000 per month and does not own any vehicle.

(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

Answer 1

Total number of families = 2400

(i) Numbers of families earning 10000 –13000 per month and owning exactly 2 vehicles = 29

Therefore, the probability that the family earning between 10000 – 13000 per month and owning exactly 2 vehicle = $\frac{29}{2400}$

(ii) Number of families earning 16000 or more per month and owning exactly 1 vehicle = 579

Therefore, the probability that the family earning between 16000 or more per month and owning exactly 1 vehicle $=\frac{579}{2400}$

(iii) Number of families earning less than 7000 per month and does not own any vehicle = 10

Therefore, the probability that the family earning less than 7000 per month and does not own any vehicle = $\frac{10}{2400}=\frac{1}{240}$

(iv) Number of families earning 13000-16000 per month and owning more than 2 vehicles = 25

Therefore, the probability that the family earning between 13000 – 16000 per month and owning more than 2 vehicles = $\frac{25}{2400}=\frac{1}{96}$

(v) Number of families owning not more than 1 vehicle = 10+160+0+305+1+535+2+469+1+579 = 2062

Therefore, the probability that the family owns not more than 1 vehicle $=\frac{2062}{2400}=\frac{1031}{1200}$