2. (a) Shade the region representing the event \(A \cup B ^ { \prime }\) on the Venn diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{01259350-0119-4500-a81b-bfa1b4234559-06_355_563_306_694} The two events \(C\) and \(D\) are mutually exclusive.
Given that \(\mathrm { P } ( C ) = \frac { 1 } { 5 }\) and \(\mathrm { P } ( D ) = \frac { 3 } { 10 }\) find
(b) (i) \(\quad \mathrm { P } ( C \cup D )\)
(ii) \(\mathrm { P } ( C \mid D )\) The two events \(F\) and \(G\) are independent.
Given that \(\mathrm { P } ( F ) = \frac { 1 } { 6 }\) and \(\mathrm { P } ( F \cup G ) = \frac { 3 } { 8 }\) find
(c) (i) \(\mathrm { P } ( G )\)
(ii) \(\mathrm { P } \left( F \mid G ^ { \prime } \right)\)