| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2020 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Probability distribution finding parameters |
| Difficulty | Easy -1.8 This is a straightforward probability question requiring only basic understanding that probability is proportional to angle. Part (a) is a simple verification (1 mark), and part (b) requires reading angles from a diagram and dividing by 360°. No problem-solving or conceptual depth—purely mechanical calculation with minimal steps. |
| Spec | 2.04a Discrete probability distributions |
| \(x\) | 1 | |||
| \(P(X = x)\) | \(\frac{5}{18}\) |
| Answer | Marks |
|---|---|
| 17(a) | Shows clearly where comes from. |
| Answer | Marks | Guidance |
|---|---|---|
| 100 | 3.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | 18 |
| Answer | Marks | Guidance |
|---|---|---|
| 17(b) | States at least one pair of | |
| (X , P(X = x)correctly | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Completes table correctly ACF | 1.1b | A1 |
| Subtotal | 2 | 12 9 12 |
| Question Total | 3 | |
| X | 2 | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Q | Marking Instructions | AO |
Question 17:
--- 17(a) ---
17(a) | Shows clearly where comes from.
5
18
Need to see and simplification.
100 | 3.1b | B1 | P(X = 1) =
100
360
=
5
360
Subtotal | 1 | 18
--- 17(b) ---
17(b) | States at least one pair of
(X , P(X = x)correctly | 1.1a | M1 | X 2 3 5
P(X = x)
5 2 1
Completes table correctly ACF | 1.1b | A1
Subtotal | 2 | 12 9 12
Question Total | 3
X | 2 | 3 | 5
P(X = x)
Q | Marking Instructions | AO | Marks | Typical SolutionA game consists of spinning a circular wheel divided into numbered sectors as shown below.
\includegraphics{figure_17}
On each spin the score, $X$, is the value shown in the sector that the arrow points to when the spinner stops.
The probability of the arrow pointing at a sector is proportional to the angle subtended at the centre by that sector.
\begin{enumerate}[label=(\alph*)]
\item Show that $P(X = 1) = \frac{5}{18}$
[1 mark]
\item Complete the probability distribution for $X$ in the table below.
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 1 & & & \\
\hline
$P(X = x)$ & $\frac{5}{18}$ & & & \\
\hline
\end{tabular}
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2020 Q17 [3]}}