2. Given that \(\mathrm { P } ( A ) = \frac { 3 } { 5 } , \mathrm { P } ( B ) = \frac { 5 } { 8 } , \mathrm { P } ( A \cap B ) = \frac { 7 } { 20 } , \mathrm { P } ( A \cup C ) = \frac { 7 } { 10 }\) and \(\mathrm { P } ( C \mid A ) = \frac { 1 } { 3 }\),

1. determine whether \(A\) and \(B\) are independent events.
2. Find \(\mathrm { P } \left( A \cap B ^ { \prime } \right)\).
3. Find \(\mathrm { P } \left( ( A \cap C ) ^ { \prime } \right)\).
4. Find \(\mathrm { P } ( A \mid C )\).