In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having either cable TV or VCR?
- 23/30
- 2/3
- 17/30
- 19/30
Answer
Let A be set of people that have Cable TV = 66%
Let B be set of people that have VCR = 20%
Both Cable TV and VCR, A ∩ B = 10%
People that have either Cable TV or VCR = (A ∪ B) - (A ∩ B)
(A ∩ B) = A + B - (A ∪ B)
(A ∪ B) = A + B - (A ∩ B)
(A ∪ B) - (A ∩ B) = A + B - 2*(A ∩ B)
= 66% + 20% - 2*10%
= 66%
The correct option is B.
