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" probability problems.
Updated On: Aug 6, 2025
- $\frac{19}{30}$
- $\frac{2}{3}$
- $\frac{17}{30}$
- $\frac{23}{30}$
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The Correct Option is A
Solution and Explanation
Using $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
$= \frac{2}{3} + \frac{1}{5} - \frac{1}{10} = \frac{20}{30} + \frac{6}{30} - \frac{3}{30} = \frac{23}{30}$. This matches option (d). Possibly a misprint in provided options.
$= \frac{2}{3} + \frac{1}{5} - \frac{1}{10} = \frac{20}{30} + \frac{6}{30} - \frac{3}{30} = \frac{23}{30}$. This matches option (d). Possibly a misprint in provided options.
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