Question
If P(A) = 0.3, P(B) = 0.4 and P(A|B) = 0.5, then what is the value of P(B|A)?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 0.325
- B. 0.333
- C. 0.375
- D. 0.667
Answer
D. 0.667
Step-by-step solution
Given P(A) = 0.3, P(B) = 0.4 and P(A|B) = 0.5. Using the formula for conditional probability: P(A|B) = P(A B) P(B) 0.5 = P(A B) 0.4 P(A B) = 0.5 0.4 = 0.2 Now, finding P(B|A): P(B|A) = P(A B) P(A) P(B|A) = 0.2 0.3 = 2 3 0.667 Answer: 0.667
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