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Math Help - Please Help me proof the equation!

  1. #1
    Yan
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    Please Help me proof the equation!

    Given three events A, B, and C such that P (A and B and C) are not equal to 0 and P(C|A and B) = P(C|B), show that P(A| B and C) = P(A|B).
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by Yan View Post
    Given three events A, B, and C such that P (A and B and C) are not equal to 0 and P(C|A and B) = P(C|B), show that P(A| B and C) = P(A|B).
    P(C/A\cap B)=\frac{P(A \cap B \cap C)}{P(A \cap B)}=\frac{P(B \cap C)}{P(B)}=P(C/B) << this is given.
    Hence \boxed{P(A \cap B \cap C)=\frac{P(A \cap B) \cdot P(B \cap C)}{P(B)}}

    P(A/ B \cap C)=\frac{P(A \cap B \cap C)}{P(B \cap C)}

    Substitute P(A\cap B\cap C) in this formula, simplify and then recall that P(A/B)=\frac{P(A \cap B)}{P(B)}
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