| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | One unknown from sum constraint only |
| Difficulty | Easy -1.8 This is a very routine probability distribution question requiring only basic recall: (a) uses the fact that probabilities sum to 1 to find a single unknown (0.2 + a + 3a + 0.4 = 1 gives a = 0.1), (b) adds two probabilities, and (c) applies independence to find P(X₁ + X₂ = 3). All three parts are standard textbook exercises with no problem-solving or insight required, making this significantly easier than average A-level questions. |
| Spec | 2.04a Discrete probability distributions |
| \(x\) | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( \mathrm { X } = \mathrm { x } )\) | 0.2 | \(a\) | \(3 a\) | 0.4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(a = 0.1\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0.5\) | B1FT | FT their \(0.1 + 0.4\); \(0 <\) their \(a <\) their \(3a < 1\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0.2 \times 0.4\) oe or their \(3a \times\) their \(a\) oe seen | B1 | \(0.2 \times 0.4\) or \(0.3 \times 0.1\) |
| \(2 \times (0.2 \times 0.4 + \text{their } 3a \times \text{their } a)\) | M1 | NB \(2 \times (0.2 \times 0.4 + 0.3 \times 0.1)\); allow omission of 2; may be implied by 0.11 |
| \(0.22\) | A1 |
## Question 6:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $a = 0.1$ | B1 | |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.5$ | B1FT | FT their $0.1 + 0.4$; $0 <$ their $a <$ their $3a < 1$ |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.2 \times 0.4$ oe or their $3a \times$ their $a$ oe seen | B1 | $0.2 \times 0.4$ **or** $0.3 \times 0.1$ |
| $2 \times (0.2 \times 0.4 + \text{their } 3a \times \text{their } a)$ | M1 | **NB** $2 \times (0.2 \times 0.4 + 0.3 \times 0.1)$; allow omission of 2; may be implied by 0.11 |
| $0.22$ | A1 | |
---6 The probability distribution of the discrete random variable $X$ is shown in the table.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | }
\hline
$x$ & 0 & 1 & 2 & 3 \\
\hline
$\mathrm { P } ( \mathrm { X } = \mathrm { x } )$ & 0.2 & $a$ & $3 a$ & 0.4 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of the constant $a$.
\item A single value of $X$ is chosen at random.
Find the probability that the value is an odd number.
\item Two independent values of $X$ are chosen at random.
Calculate the probability that the total of the two values is 3 .
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2024 Q6 [5]}}