# Math Help - Proof using Boole's Inequaility

1. ## Proof using Boole's Inequaility

Let $A_1, A_2, A_3, ...$ be a sequence of events of an experiment. Prove that $P(\displaystyle\cap_{n=1}^{\infty} A_n) \geq 1 - \displaystyle\sum_{n=1}^{\infty} P( A_n)$

Hint: Use Boole's Inequality

2. Originally Posted by Zennie
Let $A_1, A_2, A_3, ...$ be a sequence of events of an experiment. Prove that $P(\displaystyle\cap_{n=1}^{\infty} A_n) \geq 1 - \displaystyle\sum_{n=1}^{\infty} P( A_n)$

Hint: Use Boole's Inequality
I'd use $P(\cup_{n=1}^{\infty} A_n) \leq \sum_{n=1}^{\infty} P( A_n)$

and then the complement.