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Probability

Question
CBSEENMA12033627

If P( A|B) > P(A), then which of the following is correct:
  • P(B|A) < P(B) 
  • P(A ∩ B) < P(A) . P(B)
  • P(B|A) > P(B)
  • P(B|A) = P(B)

Solution

C.

P(B|A) > P(B)

P(A|B) > P(A)
 rightwards double arrow 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 greater than straight P left parenthesis straight A right parenthesis space space space space space space rightwards double arrow space space space 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 equals space straight P left parenthesis straight B right parenthesis
rightwards double arrow space space space space space straight P left parenthesis straight B space left enclose straight A right parenthesis end enclose space greater than thin space straight P left parenthesis straight B right parenthesis.
(C) is correct answer.

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