Let \(A_1,\,A_2,\,...,\,A_n\subseteq S\) be a finite collection of possibly overlapping events in some probability space. Show that
\[ P\left(\bigcap_{i=1}^n A_i\right)\geq \sum\limits_{i=1}^nP(A_i)-n+1. \]
Let \(A_1,\,A_2,\,...,\,A_n\subseteq S\) be a finite collection of possibly overlapping events in some probability space. Show that
\[ P\left(\bigcap_{i=1}^n A_i\right)\geq \sum\limits_{i=1}^nP(A_i)-n+1. \]