NDA 2025 · PYQ · Probability / Conditional probability · medium
If P(A) = 1/3, P(B) = 1/2 and P(A ∩ B) = 1/4, then what is the value of P(B | A^c)?
- A.1/8
- B.3/8✓ Correct
- C.5/8
- D.7/8
P(B|A^c) = P(B ∩ A^c)/P(A^c). P(B ∩ A^c) = P(B) - P(A ∩ B) = 1/2 - 1/4 = 1/4. P(A^c) = 1 - 1/3 = 2/3. Therefore P(B|A^c) = (1/4)/(2/3) = 3/8.
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