| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Piecewise or conditional probability function |
| Difficulty | Moderate -0.8 This is a straightforward probability distribution question requiring only basic probability axioms. Part (a) uses the fact that probabilities sum to 1 (simple algebra), and part (b) requires calculating P(N≥2) = 1 - P(N=1). Both parts are routine applications of fundamental probability concepts with minimal calculation, making this easier than average for A-level. |
| Spec | 2.04a Discrete probability distributions |
| Answer | Marks | Guidance |
|---|---|---|
| 11(a) | Finds correct value of k | AO1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | Selects relevant probability | AO1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| FT ‘their’ value of k found in part (a) | AO1.1b | A1F |
| Total | 3 | |
| Q | Marking Instructions | AO |
Question 11:
--- 11(a) ---
11(a) | Finds correct value of k | AO1.1b | B1 | 1
k =
16
(b) | Selects relevant probability | AO1.1a | M1 | P( 2 checkouts staffed)
3 3 1 1
+ k = + =
≥
16 16 16 4
ALT
P( 2 checkouts staffed)
3 1
= 1≥ − =
4 4
Finds correct probability
FT ‘their’ value of k found in part (a) | AO1.1b | A1F
Total | 3
Q | Marking Instructions | AO | Marks | Typical SolutionTerence owns a local shop. His shop has three checkouts, at least one of which is always staffed.
A regular customer observed that the probability distribution for $N$, the number of checkouts that are staffed at any given time during the spring, is
$$P(N = n) = \begin{cases}
\frac{3}{4}\left(\frac{1}{4}\right)^{n-1} & \text{for } n = 1, 2 \\
k & \text{for } n = 3
\end{cases}$$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $k$. [1 mark]
\item Find the probability that a customer, visiting Terence's shop during the spring, will find at least 2 checkouts staffed. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 Q11 [3]}}