| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | September |
| Marks | 9 |
| Topic | Independent Events |
| Type | Test independence using definition |
| Difficulty | Moderate -0.3 This is a straightforward probability question testing basic concepts (conditional probability, independence, mutual exclusivity) with standard calculations. Part (a) requires simple use of complement and conditional probability formulas, (b) is a routine independence check, (c) involves filling a Venn diagram with given constraints, and (d) is direct application of probability rules. While it requires careful bookkeeping across multiple parts, all techniques are standard A-level material with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
$P(E) = 0.25$, $P(F) = 0.4$ and $P(E \cap F) = 0.12$
\begin{enumerate}[label=(\alph*)]
\item Find $P(E'|F')$
[2 marks]
\item Explain, showing your working, whether or not $E$ and $F$ are statistically independent. Give reasons for your answer.
[2 marks]
\end{enumerate}
The event $G$ has $P(G) = 0.15$
The events $E$ and $G$ are mutually exclusive and the events $F$ and $G$ are independent.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Draw a Venn diagram to illustrate the events $E$, $F$ and $G$, giving the probabilities for each region.
[3 marks]
\item Find $P([F \cup G]')$
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q2 [9]}}