Statistics

The complement of P(B | A) is 1 - P(B | A). Is it also true that 1 - P(B | A) = P(B' | A), where B' means the complement of B?

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asked by John
  1. 1-P(B|A)
    =1-P(B∩A)/P(A)
    =( P(A)-P(B∩A) ) / P(A)
    =P(A\B)/P(A)

    P(B'|A)
    =P(B'∩A)/P(A)
    =P(A\B)/P(A)

    So yes, they are equivalent.
    =

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