| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | One unknown from sum constraint only |
| Difficulty | Moderate -0.8 Part (i) is trivial application of probabilities summing to 1. Part (ii) requires listing combinations where two independent values sum to 6 and calculating probabilities, which is straightforward but involves multiple cases. This is a standard AS-level probability question requiring only routine techniques with no conceptual challenges. |
| Spec | 2.03a Mutually exclusive and independent events2.04a Discrete probability distributions |
| \(r\) | 0 | 1 | 2 | 3 | 4 |
| P\((X = r)\) | 0.2 | 0.15 | 0.3 | \(k\) | 0.25 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (i) | 0.2 + 0.15 + 0.3 + k + 0.25 = 1 oe |
| k = 0.1 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (ii) | k2 seen |
| Answer | Marks |
|---|---|
| 0.16 | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | Or 0.3×0.25×2 seen |
| Answer | Marks |
|---|---|
| insertion of 2 | Ft k from (i) for M1M1 |
Question 4:
4 | (i) | 0.2 + 0.15 + 0.3 + k + 0.25 = 1 oe
k = 0.1 | M1
A1
[2] | 1.1
1.1
4 | (ii) | k2 seen
0.3×0.25×2 + k2
0.16 | M1
M1
A1
[3] | 3.1a
1.1
1.1 | Or 0.3×0.25×2 seen
Allow slip eg omission of 2; or
insertion of 2 | Ft k from (i) for M1M1The probability distribution of the discrete random variable $X$ is given in Fig. 4.
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$r$ & 0 & 1 & 2 & 3 & 4 \\
\hline
P$(X = r)$ & 0.2 & 0.15 & 0.3 & $k$ & 0.25 \\
\hline
\end{tabular}
Fig. 4
\begin{enumerate}[label=(\roman*)]
\item Find the value of $k$. [2]
\end{enumerate}
$X_1$ and $X_2$ are two independent values of $X$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find P$(X_1 + X_2 = 6)$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2018 Q4 [5]}}