9.
The Venn diagram, where \(p , q\) and \(r\) are probabilities, shows the events \(A , B , C\) and \(D\) and associated probabilities.
\includegraphics[max width=\textwidth, alt={}, center]{fdff6575-679e-4d25-ad43-e9d343c1746f-22_623_1130_326_438}
- State any pair of mutually exclusive events from \(A\), \(B\), \(C\) and \(D\)
The events \(B\) and \(C\) are independent.
- Find the value of \(p\)
- Find the greatest possible value of \(\mathrm { P } \left( A \mid B ^ { \prime } \right)\)
Given that \(\mathrm { P } \left( B \mid A ^ { \prime } \right) = 0.5\)
- find the value of \(q\) and the value of \(r\)
- Find \(\mathrm { P } \left( [ A \cup B ] ^ { \prime } \cap C \right)\)
- Use set notation to write an expression for the event with probability \(p\)