TITLE: How can I show that $P(A \cap B) \gt P(A) + P(B) - 1$
QUESTION [2 upvotes]: 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?

REPLY [0 votes]: $$P(A\cup B) =P(A) +P(B) - P(A\cap B)$$
$$P(S)=1 \ge P(A \cup B)$$
$$P(A∩B) \le P(A) + P(B) - 1 $$
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