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Probability

Question
CBSEENMA12033628

If A and B are any two events such that P(A) + P(B) - P(A and B) = P(A), then
  • P(B|A) = 1
  • P(A|B) = 1
  • P(B|A) = 0
  • P(A|B) = 0

Solution

B.

P(A|B) = 1 straight P left parenthesis straight A right parenthesis plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A space and space straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis
rightwards double arrow space space space space space space space space space space space space space space space straight P left parenthesis straight B right parenthesis space equals space straight P left parenthesis straight A intersection straight B right parenthesis space space space space rightwards double arrow space space space space 1 space equals 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 equals space 1 space equals space straight P left parenthesis straight A space left enclose straight B right parenthesis
∴ (B) is correct answer.

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