Conditional Probability

**chengbin** · September 13th 2009, 06:57 PM

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?

**Plato** · September 14th 2009, 03:16 AM

Originally Posted by chengbin

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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