4. \(\quad\) The events \(A\) and \(B\) are such that \(\mathrm { P } ( A ) = \frac { 2 } { 5 } , \mathrm { P } ( B ) = \frac { 1 } { 2 }\) and \(\mathrm { P } \left( A \quad B ^ { \prime } \right) = \frac { 4 } { 5 }\).

1. Find
   1. \(\mathrm { P } \left( A \cap B ^ { \prime } \right)\),
   2. \(\mathrm { P } ( A \cap B )\),
   3. \(\mathrm { P } ( A \cup B )\),
   4. \(\mathrm { P } \left( \begin{array} { l l } A & B \end{array} \right)\).
2. State, with a reason, whether or \(\operatorname { not } A\) and \(B\) are
   1. mutually exclusive,
   2. independent.