| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Principle of Inclusion/Exclusion |
| Type | Finding Set Cardinalities from Constraints |
| Difficulty | Moderate -0.3 This is a standard three-set Venn diagram problem requiring the inclusion-exclusion principle for part (a), then straightforward conditional probability calculations. While it has multiple parts and requires careful bookkeeping, the techniques are routine for Stats 1 and involve no novel problem-solving—slightly easier than average due to its mechanical nature. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03d Calculate conditional probability: from first principles |
Each of the 30 students in a class plays at least one of squash, hockey and tennis.
• 18 students play squash
• 19 students play hockey
• 17 students play tennis
• 8 students play squash and hockey
• 9 students play hockey and tennis
• 11 students play squash and tennis
\begin{enumerate}[label=(\alph*)]
\item Find the number of students who play all three sports. [3]
\end{enumerate}
A student is picked at random from the class.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Given that this student plays squash, find the probability that this student does not play hockey. [1]
\end{enumerate}
Two different students are picked at random from the class, one after the other, without replacement.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Given that the first student plays squash, find the probability that the second student plays hockey. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2017 Q11 [8]}}