6. Three events \(A , B\) and \(C\) are such that $$\mathrm { P } ( A ) = \frac { 2 } { 5 } \quad \mathrm { P } ( C ) = \frac { 1 } { 2 } \quad \mathrm { P } ( A \cup B ) = \frac { 5 } { 8 }$$ Given that \(A\) and \(C\) are mutually exclusive find

1. \(\mathrm { P } ( A \cup C )\) Given that \(A\) and \(B\) are independent
2. show that \(\mathrm { P } ( B ) = \frac { 3 } { 8 }\)
3. Find \(\mathrm { P } ( A \mid B )\) Given that \(\mathrm { P } \left( C ^ { \prime } \cap B ^ { \prime } \right) = 0.3\)
4. draw a Venn diagram to represent the events \(A , B\) and \(C\)