8 For the events \(L\) and \(M , \mathrm { P } ( L \mid M ) = 0.2 , \mathrm { P } ( M \mid L ) = 0.4\) and \(\mathrm { P } ( M ) = 0.6\).
- Find \(\mathrm { P } ( L )\) and \(\mathrm { P } \left( L ^ { \prime } \cup M ^ { \prime } \right)\).
- Given that, for the event \(N , \mathrm { P } ( N \mid ( L \cap M ) ) = 0.3\), find \(\mathrm { P } \left( L ^ { \prime } \cup M ^ { \prime } \cup N ^ { \prime } \right)\).