| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Sampling without replacement |
| Difficulty | Moderate -0.3 This is a straightforward sampling without replacement problem requiring basic counting of outcomes (5 notes choose 2 gives 10 equally likely pairs) and standard expectation/variance calculations from a given probability distribution. The verification parts guide students through the method, and the final calculations are routine applications of formulas with no conceptual challenges. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables |
| \(r\) | 10 | 15 | 20 | 25 | 30 |
| \(\mathrm { P } ( X = r )\) | 0.1 | 0.4 | 0.1 | 0.2 | 0.2 |
1 In her purse, Katharine has two $\pounds 5$ notes, two $\pounds 10$ notes and one $\pounds 20$ note. She decides to select two of these notes at random to donate to a charity. The total value of these two notes is denoted by the random variable $\pounds X$.
\begin{enumerate}[label=(\roman*)]
\item (A) Show that $\mathrm { P } ( X = 10 ) = 0.1$.\\
(B) Show that $\mathrm { P } ( X = 30 ) = 0.2$.
The table shows the probability distribution of $X$.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$r$ & 10 & 15 & 20 & 25 & 30 \\
\hline
$\mathrm { P } ( X = r )$ & 0.1 & 0.4 & 0.1 & 0.2 & 0.2 \\
\hline
\end{tabular}
\end{center}
\item Find $\mathrm { E } ( X )$ and $\operatorname { Var } ( X )$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q1 [8]}}