| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Test independence using definition |
| Difficulty | Easy -1.2 This is a straightforward probability question testing basic concepts: constructing a Venn diagram from given probabilities, checking independence using P(G∩R) = P(G)×P(R), and calculating conditional probability using P(R|G) = P(G∩R)/P(G). All calculations are routine with no problem-solving required, making it easier than average for A-level. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
In a survey, a large number of young people are asked about their exercise habits. One of these people is selected at random.
• $G$ is the event that this person goes to the gym.
• $R$ is the event that this person goes running.
You are given that P(G) = 0.24, P(R) = 0.13 and P(G ∩ R) = 0.06.
\begin{enumerate}[label=(\roman*)]
\item Draw a Venn diagram, showing the events $G$ and $R$, and fill in the probability corresponding to each of the four regions of your diagram. [3]
\item Determine whether the events $G$ and $R$ are independent. [2]
\item Find P(R | G). [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2010 Q3 [8]}}