Proof using Boole's Inequaility

• September 15th 2010, 11:13 PM
Zennie
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
• September 16th 2010, 05:10 AM
matheagle
Quote:

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.