| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Finding Set Cardinalities from Constraints |
| Difficulty | Moderate -0.3 This is a straightforward application of the inclusion-exclusion principle with all values given directly. Part (a) requires one formula application, part (b) is basic conditional probability with given information, and part (c) involves simple probability without replacement. The question is slightly easier than average as it's a standard textbook exercise with no novel insight required, though it does test multiple concepts across three parts. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables |
11 Each of the 30 students in a class plays at least one of squash, hockey and tennis.
\begin{itemize}
\item 18 students play squash
\item 19 students play hockey
\item 17 students play tennis
\item 8 students play squash and hockey
\item 9 students play hockey and tennis
\item 11 students play squash and tennis
\begin{enumerate}[label=(\alph*)]
\item Find the number of students who play all three sports.
\end{itemize}
A student is picked at random from the class.
\item Given that this student plays squash, find the probability that this student does not play hockey.
Two different students are picked at random from the class, one after the other, without replacement.
\item Given that the first student plays squash, find the probability that the second student plays hockey.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 Q11 [8]}}