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Math Help - Conditional Probability

  1. #1
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    Conditional Probability

    I don't get the multiplication theorem of conditional probability.

    p(A\cap B\cap C)=p(A) p(B\cap C|A)

    Why does it equal to

    p(A) p(B|A)p(C|A\cap B)?

    BTW, how do I get the dot for multiply in latex?
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  2. #2
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    Quote Originally Posted by chengbin View Post
    I don't get the multiplication theorem of conditional probability.

    p(A\cap B\cap C)=p(A) p(B\cap C|A)

    Why does it equal to p(A) p(B|A)p(C|A\cap B)?

    BTW, how do I get the dot for multiply in latex?
    [tex]A \cdot B[/tex] gives A \cdot B.

    If P(L)\not= 0 then by definition P(K|L)=\frac{P(K\cap L)}{P(L)}.
    But that means P(K\cap L)=P(K|L)\cdot P(L).
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