The survey has been undertaken to determine whether there is a relationship between the place of residence and ownership of an automobile. A random sample of car owners, 200 from large cities, 150 from suburbs and 150 from rural areas were selected and tabulated as follow
If a car owner was selected at random, what is the probability that he/she
(i) owns a foreign car.
(ii) owns a foreign car and lives in a suburb.
(iii) lives in a large city and does not own a foreign car.
(iv) lives in large city and owns a foreign car.
(v) neither lives in a rural area nor owns a foreign car.
(i) Total car owners = 500
Owners of foreign cars = 90 + 60 + 25 = 175
⇒ 
(ii) Total car owners = 500
Owners of foreign cars living in suburb = 60
⇒ 
(iii) Total car owners = 500
Owners of cars which is not foreign and live in large city = 110
⇒ 
(iv) Total car owners = 500
Owners of foreign cars living in large cities = 90
⇒ 
(v) Total car owners = 500
Owners not living in rural areas belongs to 4 different categories
(a) foreign car-Large City
(b) foreign car-Suburb
(c) non-foreign car-Large City
(d) non-foreign car-Suburb
Now, according to the question, among these four categories the owners should also not own a foreign car.
∴ we now have 2 categories left
(c) non-foreign car-Large City
(d) non-foreign car-Suburb
No. of owners in category (c) = 110
No. of owners in category (d) = 90
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
