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If A and B are events such that P(A|B) = P(B|A), then which of the following is true?

(A) A $\subset$ B but A $\neq$ B (B) A = B (C) A $\cap$ B = Null (D) P(A) = P(B)

1 Answer

  • Given P(E), P(F), P(E $\cap$ F), P(E/F) $= \large \frac{P(E \;\cap \;F)}{P(F)}$
P(A/B) $= \large \frac{P(A \;\cap \;B)}{P(B)}$ and P(B/A) $= \large \frac{P(A \;\cap \;B)}{P(A)}$
For P(A/B) to be equal to P(B/A), P(A/B) $= \large \frac{P(A \;\cap \;B)}{P(B)}$ must be equal to P(B/A) $= \large \frac{P(A \;\cap \;B)}{P(A)}$
Simplifying we get P(B) = P(A) must be true for the original condition to be true.
Solution: (D) P(A) = P(B).
answered Mar 5, 2013 by poojasapani_1
edited Jun 18, 2013 by balaji.thirumalai