5. Two events C and D are such that \(P ( C \mid D ) = 3 \times P ( C )\) where \(P ( C ) \neq 0\).
- Explain whether or not events C and D could be independent events.
Given also that
$$P ( C \cap D ) = \frac { 1 } { 2 } \times P ( C ) \text { and } P \left( C ^ { \prime } \cap D ^ { \prime } \right) = \frac { 7 } { 10 }$$
- find \(P ( C )\), showing your working clearly.