I wonder if it is ture that $P(A\cap B) \geq P(A) \times P(B)$ for any two events?
My observations so far are:
When $A \subseteq B$, $P(A\cap B) = P(A) \geq P(A) \times P(B)$.
When $B = \Omega$, $P(A\cap B) = P(A) = P(A) \times P(B)$.
Can there be an equality relation between $P(A\cap B)$ and $P(A) \times P(B)$, just like the inclusion and exclusion relation between $P(A\cup B)$ and $P(A) + P(B)$?
Thanks!