| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Test independence using definition |
| Difficulty | Moderate -0.8 This is a straightforward S1 probability question requiring basic counting from a given table and checking independence using P(A∩B) = P(A)P(B). Part (i) is simple counting, and part (ii) involves routine calculation of three probabilities with no conceptual difficulty—easier than average A-level. |
| Spec | 2.03a Mutually exclusive and independent events |
| Score on second die | ||||
| 1 | 2 | 3 | 4 | |
| \multirow{4}{*}{\rotatebox{90}{Score on first die}} 1 | 1 | 2 | 3 | 4 |
| \cline{2-5} 2 | 2 | 4 | 6 | 8 |
| \cline{2-5} 3 | 3 | 6 | 9 | 12 |
| \cline{2-5} 4 | 4 | 8 | 12 | 16 |
The table shows all the possible products of the scores on two fair four-sided dice.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
\multicolumn{5}{|c|}{Score on second die} \\
\hline
& 1 & 2 & 3 & 4 \\
\hline
\multirow{4}{*}{\rotatebox{90}{Score on first die}} 1 & 1 & 2 & 3 & 4 \\
\cline{2-5}
2 & 2 & 4 & 6 & 8 \\
\cline{2-5}
3 & 3 & 6 & 9 & 12 \\
\cline{2-5}
4 & 4 & 8 & 12 & 16 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Find the probability that the product of the two scores is less than 10. [1]
\item Show that the events 'the score on the first die is even' and 'the product of the scores on the two dice is less than 10' are not independent. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2011 Q2 [4]}}