| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | February |
| Marks | 8 |
| Topic | Conditional Probability |
| Type | Venn diagram with three events |
| Difficulty | Standard +0.3 This is a structured Venn diagram probability question requiring systematic application of standard probability rules (mutually exclusive events, independence, conditional probability). While it has multiple parts and requires careful bookkeeping, each step follows directly from basic probability definitions without requiring problem-solving insight or novel approaches. Slightly easier than average due to its guided, sequential nature. |
| Spec | 2.03a Mutually exclusive and independent events2.03d Calculate conditional probability: from first principles |
The Venn diagram shows the probabilities associated with four events, $A$, $B$, $C$ and $D$
\includegraphics{figure_3}
\begin{enumerate}[label=(\alph*)]
\item Write down any pair of mutually exclusive events from $A$, $B$, $C$ and $D$
[1]
\item Given that $P(B) = 0.4$
find the value of $p$
[1]
\item Given also that $A$ and $B$ are independent
find the value of $q$
[2]
\item Given further that $P(B'|C) = 0.64$
find
\begin{enumerate}[label=(\roman*)]
\item the value of $r$
\item the value of $s$
\end{enumerate}
[4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2021 Q3 [8]}}