Misc 1 - Find P(B|A), if (i) A is a subset of B - Class 12 - Miscellaneous

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  1. Chapter 13 Class 12 Probability
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Misc 1 A and B are two events such that P (A) ≠ 0. Find P(B|A), if (i) A is a subset of B Since A is a subset of B So, A ⊂ B ∴ A ∩ B = A So, P(A ∩ B) = P(A) Now, P(B|A) = 𝑃(𝐵 ∩ 𝐴)﷮𝑃(𝐴)﷯ = 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐴)﷯ = 𝑃(𝐴)﷮𝑃(𝐴)﷯ = 1 ∴ P(B|A) = 1 Misc 1 A and B are two events such that P (A) ≠ 0. Find P(B|A), if (ii) A ∩ B = φ A ∩ B = φ P(A ∩ B) = 0 P(B|A) = 𝑃(𝐵 ∩ 𝐴)﷮𝑃(𝐴)﷯ = 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐴)﷯ = 0﷮𝑃(𝐴)﷯ = 0 ∴ P(B|A) = 0

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