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Question:

In a certain town, 25% of the families own a phone.

All (a), (b) and (c) are correct.

Only (a) and (b) are correct.

Only (a) and (c) are correct.

Only (b) and (c) are correct.

Solution:

Let A be the set of people who own a phone and B be the set of people who own a car.

p(A) = 25/100, p(B) = 15/100
p(A'∩B') = 65/100 and n(A∩B) = 2000
⇒p(A∪B)' = 65/100 ⇒p(A∪B) = 35/100 ———(1)
p(A∪B) = p(A) + p(B) - p(A∩B) ⇒p(A∩B) = 5/100 ———(2)
If x be the total no. of people then
5/100 x = 2000 ∴x = 40000 ———(3)
From (1), (2) and (3)
All (a),(b) and (c) are correct.
Hence, option A.