# Conditional Probability

• Sep 13th 2009, 06:57 PM
chengbin
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?
• Sep 14th 2009, 03:16 AM
Plato
Quote:

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?

$$A \cdot B$$ 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 $P(K\cap L)=P(K|L)\cdot P(L)$.