If A and B are two events such that P(A) ≠ P(B), P(A) > 0, P(B) > 0, and P(A|B) = P(B|A), then it must be true that:
If A and B are two events such that P(A) ≠ P(B), P(A) > 0, P(B) > 0, and P(A|B) = P(B|A), then it must be true that:
- A. A ⊂ B
- B. B ⊂ A
- C. P(A∩B) = 0
- D. Such a case is mathematically impossible
Answer: C) P(A∩B) = 0
Explanation: P(A|B) = P(B|A) → P(A∩B)/P(B) = P(A∩B)/P(A). Since P(A) ≠ P(B), this equation can only hold if P(A∩B) = 0.
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