Working through some probability theory sample questions from my course notes and I'm having difficulty trying to prove this probability theorem:
Let $A_1$, $A_2$, $\ldots$, $A_n$ be events in the sample space $\Omega$ with probability measure P. Show that:
P($A_1\bigcap$ $A_2\bigcap\ldots\bigcap$ $A_n$) $\ge$ P( $A_1$) + P( $A_2$) + $\ldots$ + P( $A_n$) - (n - 1)
Any help with this would be greatly appreciated. Even a hint as to where to start. I'd like to figure it out on my own, so that I can understand it in full detail, but I am really stuck atm.