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Math Help - Simple probability proof using conditional probabilities

  1. #1
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    Simple probability proof using conditional probabilities

    Im terrible at proofs....

    Use the definition of conditional probabilities to prove that any events A, B, C, D, E and F,

    P(A \capB \capC \capD \capE \capF) = P(A \capB \capC \capD \midE \capF)P(E \capF)

    and P(A \capB \capC \capD \capE \capF) = P(A \capB \midC \capD \capE \capF)P(C \capD \capE \midF)P(F)

    Also, can anyone form a similar identity?
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  2. #2
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    they all come from the definition of conditional probability:
    P(A | B) = \frac{P(A \cap B)}{P(B)} \Rightarrow P(A \cap B) = P(A|B)P(B)
    and the associative law of intersection of sets:
     (A \cap B) \cap C = A \cap ( B \cap C )
    The last law allaws you to write the left or right side of the equality as  A \cap B \cap C
    Last edited by johanS; February 13th 2010 at 06:28 AM.
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