7. (a) Given that \(\mathrm { P } ( A ) = a\) and \(\mathrm { P } ( B ) = b\) express \(\mathrm { P } ( A \cup B )\) in terms of \(a\) and \(b\) when
- \(A\) and \(B\) are mutually exclusive,
- \(A\) and \(B\) are independent.
Two events \(R\) and \(Q\) are such that
\(\mathrm { P } \left( R \cap Q ^ { \prime } \right) = 0.15 , \quad \mathrm { P } ( Q ) = 0.35\) and \(\mathrm { P } ( R \mid Q ) = 0.1\)
Find the value of
(b) \(\mathrm { P } ( R \cup Q )\),
(c) \(\mathrm { P } ( R \cap Q )\),
(d) \(\mathrm { P } ( R )\).