| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Three-Set Venn Diagram Probability Calculation |
| Difficulty | Moderate -0.8 This is a straightforward Venn diagram probability question requiring basic reading of the diagram, addition of regions, conditional probability using P(A|B) = P(A∩B)/P(B), and a simple binomial calculation (1-p)^3. All techniques are standard S1 content with no problem-solving insight needed, making it easier than average but not trivial due to the multi-part structure and 8 total marks. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
A survey is being carried out into the carbon footprint of individual citizens. As part of the survey, 100 citizens are asked whether they have attempted to reduce their carbon footprint by any of the following methods.
\begin{itemize}
\item Reducing car use
\item Insulating their homes
\item Avoiding air travel
\end{itemize}
The numbers of citizens who have used each of these methods are shown in the Venn diagram.
\includegraphics{figure_6}
One of the citizens is selected at random.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that this citizen
\begin{enumerate}[label=(\alph*)]
\item has avoided air travel, [1]
\item has used at least two of the three methods. [2]
\end{enumerate}
\item Given that the citizen has avoided air travel, find the probability that this citizen has reduced car use. [2]
\end{enumerate}
Three of the citizens are selected at random.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Find the probability that none of them have avoided air travel. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2011 Q6 [8]}}