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 chosen is 

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

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

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

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

(v) owning not more than 1 vehicle.

Answer 1

Total no. of families considered = 2400 

(i) P(a family earning Rs 10000 – 13000 per month and owning exactly 2 vehicles) 

= No. of families earning Rs 10000 – 13000 per month and owning 2 vehicles /Total no. of families = 29 / 2400

(ii) P (a family earning Rs 16000 or more per month and owning exactly 1 vehicle)

= No. of families earning Rs 16000 or more per month and owning 1 vehicle/ Total no. of families = 579/ 193 = 2400/ 800

(iii) P(a family earning less than Rs 7000 per month and does not own any vehicle) 

= No. of families earning less than Rs 7000 per month and does not own any vehicle /Total no. of families = 10 / 2400 = 1 / 240

(iv) P(a family earning Rs 13000 – 16000 per month and owing more than 2 vehicles) 

= No. of families earning Rs 13000 – 16000 per month and owning more than 2 vehicles / Total no. of families 

= 25/ 2400 = 1 /96

(v) P (a family owning 0 vehicle or 1 vehicle) = P (a family not owning more than 1 vehicle)

= (10 +0+ 1+ 2+ 1+ 160+ 305+ 535+ 469+ 579) / 2400  

= 2062 /  2400 = 1031/ 1200