NDA 2025 · PYQ · Probability / De Morgan's law · easy
If P(A) = 1/3, P(B) = 1/2 and P(A ∩ B) = 1/4, then what is the value of P(A^c ∩ B^c)?
- A.1/4
- B.5/12✓ Correct
- C.7/12
- D.11/12
By De Morgan's law, P(A^c ∩ B^c) = P((A ∪ B)^c) = 1 - P(A ∪ B). P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 1/3 + 1/2 - 1/4. Common denominator 12: 4/12 + 6/12 - 3/12 = 7/12. Therefore P(A^c ∩ B^c) = 1 - 7/12 = 5/12.
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