Question: For three events, A, B, and C, with P(C) > 0, we have P(A c |C) = 1 P(A|C); P(|C) = 0; P(A|C) 1;

For three events, A, B, and C, with P(C) > 0, we have

  • P(Ac|C) = 1 −P(A|C);
  • P(∅|C) = 0;
  • P(A|C) ≤ 1;
  • P(A −B|C) = P(A|C) −P(A ∩ B|C);
  • P(A ∪ B|C) = P(A|C) +P(B|C) −P(A ∩ B|C);
  • if A ⊂ B then P(A|C) ≤ P(B|C).

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