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.
Monthly income Vehicles per family
(in Rs.) 0 1 2 Above 2
Less than 7000 10 160 25 0
7000 - 10000 0 305 27 2
10000 - 13000 1 535 29 1
13000-16000 2 469 59 25
16000 or more 1 579 82 88
Suppose a family is chosen. Find the probability that the family chosen is
a) Earning `10000-13000 per month and owing exactly 2 vehicles.
b) Earning `16000 or more per month and owing exactly 1 vehicle.
c) Earning less than `7000 per month and does not own any vehicle.
d) Earning `13000
- 16000 per month and owing more than 2 vehicles.
Answers
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
Answer:
Please refer the image
