The Venn diagram shows three events \(A , B\) and \(C\), where \(p , q , r , s\) and \(t\) are probabilities.
\includegraphics[max width=\textwidth, alt={}, center]{319667e7-3f8b-4a33-8fc5-ef72154d1421-10_647_972_306_488}
(b) Find the value of \(r\).
(c) Hence write down the value of \(s\) and the value of \(t\).
(d) State, giving a reason, whether or not the events \(A\) and \(B\) are independent.
(e) Find \(\mathrm { P } ( B \mid A \cup C )\).
\(\mathrm { P } ( A ) = 0.5 , \mathrm { P } ( B ) = 0.6\) and \(\mathrm { P } ( C ) = 0.25\) and the events \(B\) and \(C\) are independent.
(a) Find the value of \(p\) and the value of \(q\).