Ex 13.1, 17 - If A and B are events such that P(A|B) = P(B|A)

  1. Chapter 13 Class 12 Probability (Term 2)
  2. Concept wise

Transcript

Ex 13.1, 17 If A and B are events such that P(A|B) = P(B|A), then (A) A βŠ‚ B but A β‰  B (B) A = B (C) A ∩ B = Ο† (D) P(A) = P(B)Given P(A|B) = P(B|A) (𝑃(𝐴 ∩ 𝐡))/(𝑃(𝐴)) = (𝑃(𝐡 ∩ 𝐴))/(𝑃(𝐡)) (𝑃(𝐴 ∩ 𝐡))/(𝑃(𝐴)) = (𝑃(𝐴 ∩ 𝐡))/(𝑃(𝐡)) 1/(𝑃(𝐴)) = 1/(𝑃(𝐡)) ∴ "P(A) = P(B)" So, option (D) is correct (Since "P(B"∩"A)" = "P(A"∩"B) ")

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