| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Three Events with Independence Constraints |
| Difficulty | Moderate -0.5 Part (a) tests basic probability definitions (mutually exclusive and independence) requiring simple recall. Parts (b)-(d) involve standard S1 probability calculations using Venn diagram relationships and conditional probability, but the logic is straightforward once you identify P(R∩Q) = P(R|Q)×P(Q) = 0.035, then use P(R) = P(R∩Q') + P(R∩Q). This is slightly easier than average due to being a routine multi-part question with clear signposting and no conceptual surprises. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
7. (a) Given that $\mathrm { P } ( A ) = a$ and $\mathrm { P } ( B ) = b$ express $\mathrm { P } ( A \cup B )$ in terms of $a$ and $b$ when
\begin{enumerate}[label=(\roman*)]
\item $A$ and $B$ are mutually exclusive,
\item $A$ and $B$ are independent.
Two events $R$ and $Q$ are such that\\
$\mathrm { P } \left( R \cap Q ^ { \prime } \right) = 0.15 , \quad \mathrm { P } ( Q ) = 0.35$ and $\mathrm { P } ( R \mid Q ) = 0.1$\\
Find the value of\\
(b) $\mathrm { P } ( R \cup Q )$,\\
(c) $\mathrm { P } ( R \cap Q )$,\\
(d) $\mathrm { P } ( R )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2009 Q7 [7]}}