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 (in Rs.)Vehicles per family
012Above 2
Less than 700010160250
7000 - 100000305272
10000 - 130001535291
1300 - 1600024695925
1600 or more15798288
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 I 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 :

Number of total families surveyed
= 10 + 160 + 25 + 0 + 0 + 305 + 27 + 2 + 1 + 535 + 29 + 1 + 2 + 469 + 59 + 25 + 1 + 579 + 82 + 88 = 2400

i) Number of families earning Rs. 10000 - 13000 per month and owning exactly 2 vehicles = 29
Hence, required probability is \(P = \frac{579}{2400}\)

ii) Number Of families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579
Hence, required probability is \(P = \frac{10}{2400} =\frac{1}{240}\)

iii) Number of families earning less than Rs. 7000 per month and dcmas not own any vehicle = 10
Hence, required probability is \(P = \frac{10}{2400} =\frac{1}{240}\)

iv) Number of families earning Rs. 13000 - 16000 per month and owning more than 2 vehicles = 25
Hence, required probability is \(P = \frac{25}{2400} = \frac{1}{96}\)

v)Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 535 + 2 + 469 + 1 + 579 = 2062
Hence, required probability is \(P = \frac{2026}{2400} = \frac{1013}{1200}\)

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