Question:
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?
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?
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Use inclusion-exclusion formula for “either-or” type set problems.
Updated On: Jul 24, 2025
- 19/30
- 2/3
- 17/30
- 23/30
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The Correct Option is D
Solution and Explanation
Step 1: Let total number of people = 1 (for simplicity)
Step 2: People with Cable TV = 2/3
Step 3: People with VCR = 1/5
Step 4: People with both Cable TV and VCR = 1/10
Step 5: Use inclusion-exclusion:
P(C ∪ V) = P(C) + P(V) − P(C ∩ V)
= 2/3 + 1/5 − 1/10
= (20 + 6 − 3)/30 = 23/30
Step 6: So, fraction having either = 23/30
Step 2: People with Cable TV = 2/3
Step 3: People with VCR = 1/5
Step 4: People with both Cable TV and VCR = 1/10
Step 5: Use inclusion-exclusion:
P(C ∪ V) = P(C) + P(V) − P(C ∩ V)
= 2/3 + 1/5 − 1/10
= (20 + 6 − 3)/30 = 23/30
Step 6: So, fraction having either = 23/30
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