| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Piecewise or conditional probability function |
| Difficulty | Moderate -0.3 This is a straightforward probability distribution question requiring basic algebraic manipulation. Part (a) involves summing probabilities to equal 1 (routine application of a fundamental property), and part (b) requires solving simultaneous equations using the given condition. Both parts are standard textbook exercises with clear methods and minimal problem-solving insight needed. |
| Spec | 2.04a Discrete probability distributions |
| Answer | Marks |
|---|---|
| 16(a) | Substitutes x values |
| Answer | Marks | Guidance |
|---|---|---|
| of c | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| OE | 2.1 | R1 |
| Subtotal | 2 | |
| x | 0 | 1 |
| P(X=x) | 7c | 5c |
| Q | Marking Instructions | AO |
| Answer | Marks |
|---|---|
| 16(b) | Forms a second |
| Answer | Marks | Guidance |
|---|---|---|
| P(X=3) and P(X=4) | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| OE | 1.1b | A1 |
| Subtotal | 2 | |
| Question Total | 4 | |
| Q | Marking Instructions | AO |
Question 16:
--- 16(a) ---
16(a) | Substitutes x values
into probability
function to obtain at
least three correct
expressions in terms
of c | 1.1a | M1 | x 0 1 2 3 4
P(X=x) 7c 5c 3c c k
7c + 5c + 3c + c + k = 1
16c + k = 1
Completes rigorous
argument by obtaining
five correct
expressions and
summing them to 1 to
obtain required result
OE | 2.1 | R1
Subtotal | 2
x | 0 | 1 | 2 | 3 | 4
P(X=x) | 7c | 5c | 3c | c | k
Q | Marking Instructions | AO | Marks | Typical Solution
--- 16(b) ---
16(b) | Forms a second
equation using their
expressions for
P(X=3) and P(X=4) | 1.1a | M1 | 5
c+k =
8
1 3
c= k =
40 5
Obtains
3
c= 1 andk =
40 5
OE | 1.1b | A1
Subtotal | 2
Question Total | 4
Q | Marking Instructions | AO | Marks | Typical SolutionThe discrete random variable $X$ has the probability function
$$P(X = x) = \begin{cases}
c(7 - 2x) & x = 0, 1, 2, 3 \\
k & x = 4 \\
0 & \text{otherwise}
\end{cases}$$
where $c$ and $k$ are constants.
\begin{enumerate}[label=(\alph*)]
\item Show that $16c + k = 1$
[2 marks]
\item Given that $P(X \geq 3) = \frac{5}{8}$
find the value of $c$ and the value of $k$.
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2021 Q16 [4]}}