Question
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)?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 1 8
- B. 3 8
- C. 5 8
- D. 7 8
Answer
B. 3 8
Step-by-step solution
The conditional probability is given by: P(B | A^c) = P(B A^c) P(A^c) The probability of the complement of A is: P(A^c) = 1 - P(A) = 1 - 1 3 = 2 3 The probability of B A^c is: P(B A^c) = P(B) - P(A B) = 1 2 - 1 4 = 1 4 Substituting these values into the formula: P(B | A^c) = 1 4 2 3 = 3 8 Answer: 3 8
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