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# If a and B Are Events Such that P (A|B) = P(B|A), Then - CBSE (Commerce) Class 12 - Mathematics

ConceptProperties of Conditional Probability

#### Question

If A and B are events such that P (A|B) = P(B|A), then

(A) A ⊂ B but A ≠ B

(B) A = B

(C) A ∩ B = Φ

(D) P(A) = P(B)

#### Solution

It is given that, P(A|B) = P(B|A)

=> (P (A ∩ B))/(P(B)) = (P (A ∩ B))/(P(A))

⇒ P (A) = P (B)

Thus, the correct answer is D.

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#### APPEARS IN

Solution If a and B Are Events Such that P (A|B) = P(B|A), Then Concept: Properties of Conditional Probability.
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