Edexcel S1 2013 June — Question 6

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2013
SessionJune
TopicConditional Probability
TypeConditional probability with algebraic expressions

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4cf4f2d7-d912-4b65-a666-caa37009661a-11_606_1131_210_411} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The Venn diagram in Figure 1 shows three events \(A , B\) and \(C\) and the probabilities associated with each region of \(B\). The constants \(p , q\) and \(r\) each represent probabilities associated with the three separate regions outside \(B\). The events \(A\) and \(B\) are independent.
  1. Find the value of \(p\). Given that \(\mathrm { P } ( B \mid C ) = \frac { 5 } { 11 }\)
  2. find the value of \(q\) and the value of \(r\).
  3. Find \(\mathrm { P } ( A \cup C \mid B )\).