| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Simple algebraic expression for P(X=x) |
| Difficulty | Easy -1.2 This is a straightforward AS-level probability distribution question requiring only basic probability axioms. Part (a) involves summing probabilities to equal 1 and solving a simple linear equation. Part (b) requires either direct calculation or using the complement rule. Both parts are routine applications with no problem-solving insight needed. |
| Spec | 2.04a Discrete probability distributions |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(4c + 3c + 2c + c = 1 \Rightarrow 10c = 1 \Rightarrow c = \frac{1}{10}\) | M1 | Substitutes \(x\) values into formula, at least 3 terms correct in terms of \(c\). ACF. NB: using \(c=\frac{1}{10}\) and showing four probabilities sum to 1 scores max M1R0 |
| Equates sum to 1 and shows convincingly that \(c = \frac{1}{10}\) | R1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(3c + 2c + c = 6c\); \(P(X \geq 1) = 0.6\) | M1 | Adds probabilities for \(x=1,2,3\) (can be in terms of \(c\)), or states \(P(X=0)=4c\) and subtracts from 1 |
| \(P(X \geq 1) = 0.6\) | A1 | CAO ACF |
## Question 14(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $4c + 3c + 2c + c = 1 \Rightarrow 10c = 1 \Rightarrow c = \frac{1}{10}$ | M1 | Substitutes $x$ values into formula, at least 3 terms correct in terms of $c$. ACF. NB: using $c=\frac{1}{10}$ and showing four probabilities sum to 1 scores max M1R0 |
| Equates sum to 1 and shows convincingly that $c = \frac{1}{10}$ | R1 | |
## Question 14(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $3c + 2c + c = 6c$; $P(X \geq 1) = 0.6$ | M1 | Adds probabilities for $x=1,2,3$ (can be in terms of $c$), or states $P(X=0)=4c$ and subtracts from 1 |
| $P(X \geq 1) = 0.6$ | A1 | CAO ACF |14 A probability distribution is given by
$$\mathrm { P } ( X = x ) = c ( 4 - x ) , \text { for } x = 0,1,2,3$$
where $c$ is a constant.\\
14
\begin{enumerate}[label=(\alph*)]
\item Show that $c = \frac { 1 } { 10 }$\\
14
\item Calculate $\mathrm { P } ( X \geq 1 )$
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2019 Q14 [4]}}