Let \(A,\,B\subseteq S\) be any pair of events in a sample space \(S\), and show that
\[ \max\{0,\,P(A)+P(B)-1\}\leq P(A\cap B)\leq\min\{P(A),\,P(B)\}. \]
Let \(A,\,B\subseteq S\) be any pair of events in a sample space \(S\), and show that
\[ \max\{0,\,P(A)+P(B)-1\}\leq P(A\cap B)\leq\min\{P(A),\,P(B)\}. \]