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?

The inequality is not correct, for example, let $A$ be the event that you get a head and $B$ be the even that you get a tail.
$$P(A \cap B)=0$$
$$P(A)+P(B)-1=0$$
$$0> 0$$ which is a contradiction.
