Question

If A and B are events such that P(A|B) = P(B|A), then
A ⊂ B but A ≠ B
A = B
A ∩ B = ϕ
P(A) = P(B)

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Solution

P(A) = P(B)

straight P left parenthesis straight A space left enclose straight B right parenthesis space equals space straight P left parenthesis straight B space left enclose straight A right parenthesis

rightwards double arrow space space space space space space space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals space fraction numerator straight P left parenthesis straight B intersection straight A right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction rightwards double arrow space space space space space space space space fraction numerator straight P left parenthesis straight A space intersection space straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space straight A space intersection space straight B space equals space straight B space intersection straight A close square brackets rightwards double arrow space space space space space space straight P left parenthesis straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space space space space space rightwards double arrow space space space straight P left parenthesis straight A right parenthesis space equals space straight P left parenthesis straight B right parenthesis

∴ (D) is correct answer.

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Probability

If A and B are events such that P(A|B) = P(B|A), then
A ⊂ B but A ≠ B
A = B
A ∩ B = ϕ
P(A) = P(B)

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Mock Test Series

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Probability

If A and B are events such that P(A|B) = P(B|A), then A ⊂ B but A ≠ B A = B A ∩ B = ϕ P(A) = P(B)

Some More Questions From Probability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If A and B are events such that P(A|B) = P(B|A), then
A ⊂ B but A ≠ B
A = B
A ∩ B = ϕ
P(A) = P(B)