Let A and B be two events. Prove that $\displaystyle P(AB) \geq P(A) + P(B) - 1$
Assuming $\displaystyle P(AB)$ means $\displaystyle P(A\cup B)$, use that $\displaystyle P(A\cup B) = P(A) + P(B) - P(A \cap B)$ and that $\displaystyle 0\le P(X) \le1$ for any event $\displaystyle \,X$.