Question
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)?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 1 4
- B. 5 12
- C. 7 12
- D. 11 12
Answer
B. 5 12
Step-by-step solution
Using the formula for the probability of the union of two events: P(A B) = P(A) + P(B) - P(A B) Substituting the given values: P(A B) = 1 3 + 1 2 - 1 4 P(A B) = 4 + 6 - 3 12 = 7 12 By De Morgan's laws, A^c B^c = (A B)^c. Therefore, the probability is: P(A^c B^c) = 1 - P(A B) P(A^c B^c) = 1 - 7 12 = 5 12
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