| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Two-item selection from population |
| Difficulty | Easy -1.8 This is a straightforward probability question requiring basic Venn diagram reading and simple probability calculations. Part (a) is direct reading and division. Part (b) involves conditional probability with replacement from a subset, using basic counting principles—routine S1/statistics content with no conceptual challenges. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables |
In a survey, 50 people were asked whether they had passed A-level English and whether they had passed A-level Mathematics.
The numbers of people in various categories are shown in the Venn diagram.
\includegraphics{figure_4}
\begin{enumerate}[label=(\alph*)]
\item A person is chosen at random from the 50 people.
Find the probability that this person has passed A-level Mathematics. [1]
\item Two people are chosen at random, without replacement, from those who have passed A-level in at least one of the two subjects.
Determine the probability that both of these people have passed A-level Mathematics. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q9 [4]}}