# Math Help - Quick probability proof

1. ## Quick probability proof

Let A and B be two events. Prove that $P(AB) \geq P(A) + P(B) - 1$

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

3. Sorry for the lack of clarity.

$P(AB)$ means $P(A \cap B)$. So prove that $P(A \cap B) \geq P(A) + P(B) - 1$

4. Originally Posted by Zennie
Sorry for the lack of clarity.

$P(AB)$ means $P(A \cap B)$. So prove that $P(A \cap B) \geq P(A) + P(B) - 1$
If you solve for $P(A \cap B)$ you'll see it works out the same.