| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2026 |
| Session | January |
| Marks | 11 |
| Topic | Probability Definitions |
| Type | Venn diagram completion |
| Difficulty | Standard +0.3 This is a multi-part Venn diagram question requiring understanding of probability definitions (mutual exclusivity, independence, conditional probability) and set notation. While it has several parts, each involves standard probability formulas and algebraic manipulation. The independence condition in part (b) and conditional probability in part (d) require careful setup but are routine A-level techniques. This is slightly easier than average due to the structured, guided nature of the parts. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
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}
\begin{enumerate}[label=(\alph*)]
\item State any pair of mutually exclusive events from $A$, $B$, $C$ and $D$
The events $B$ and $C$ are independent.
\item Find the value of $p$
\item Find the greatest possible value of $\mathrm { P } \left( A \mid B ^ { \prime } \right)$
Given that $\mathrm { P } \left( B \mid A ^ { \prime } \right) = 0.5$
\item find the value of $q$ and the value of $r$
\item Find $\mathrm { P } \left( [ A \cup B ] ^ { \prime } \cap C \right)$
\item Use set notation to write an expression for the event with probability $p$
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2026 Q9 [11]}}