How can I show that $P(A \cap B) \gt P(A) + P(B) - 1$ How can I show that $P(A \cap B) \gt P(A) + P(B) - 1$
I know that
$P(A \cap B)= P(A)P(B)$
But I don't see how that can help me get to that inequality.
Can someone give me a hint on how to start this?

$$P(A\cap B)-P(A)-P(B)+1=P(A)P(B)-P(A)-P(B)+1=$$
$$=\left(1-P(A)\right)\left(1-P(B)\right)\geq0$$
