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Misc 17 - If P(B|A) = 1 - Chapter 13 Class 12 Probability CBSE - Conditional Probability - Values given

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  1. Chapter 13 Class 12 Probability
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Misc 17 If A and B are two events such that P(A) ≠ 0 and P(B|A) = 1, then (A) A ⊂ B (B) B ⊂ A (C) B = φ (D) A = φ Given P(B|A) = 1 i.e. 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐴)﷯=1 𝑃 𝐴∩𝐵﷯=𝑃(𝐴) Option A: A ⊂ B A∩B=A So, P A∩B﷯=P(A) Hence Option A is Correct. Option B: B ⊂ A B ∩ A = B So, P(B ∩ A) = P(B) i.e. P(A ∩ B) = P(B) Hence option B is incorrect. Option C: B = φ ⇒ P(B) = 0 So, P(A) = 1 Since, B = φ ∴ P(A ∩ B) = 0 So, P(A ∩ B) ≠ P(A) Hence option C is Incorrect. Option D: A = φ So, P(A) = 0 But given P(A) ≠ 0 Hence option D is incorrect .

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