| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2023 |
| 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) sum probabilities to 1 and solve 10p=1, (b) add three probabilities, (c) apply binomial distribution formula with given n and p. All three parts are standard textbook exercises with no problem-solving or conceptual challenge beyond direct application of definitions. |
| Spec | 2.04a Discrete probability distributions2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| \(x\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| \(\mathrm { P } ( X = x )\) | \(p\) | \(p\) | \(p\) | \(p\) | \(p\) | \(p\) | \(p\) | \(3 p\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(7p + 3p = 1\) oe | M1 (1.2) | must see some reasoning; allow explanation in words |
| \(p = 0.1\) or \(\frac{1}{10}\) isw cao | A1 (1.1) | if unsupported, allow SC1 for correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.7\) or \(\frac{7}{10}\) | B1FT (1.1) | their \(7p\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(B(30, \text{their } 0.3)\) seen or used | M1 (1.1) | FT their \(3p\); allow M1 for \((\text{their } 0.3)^2 \times (\text{their } 0.7)^{28}\) |
| awrt \(0.0018\) isw | A1 (1.1) | not from wrong working; if unsupported, allow SC1 for correct answer |
## Question 4(a):
$7p + 3p = 1$ oe | M1 (1.2) | must see some reasoning; allow explanation in words
$p = 0.1$ or $\frac{1}{10}$ isw cao | A1 (1.1) | if unsupported, allow SC1 for correct answer
## Question 4(b):
$0.7$ or $\frac{7}{10}$ | B1FT (1.1) | their $7p$
## Question 4(c):
$B(30, \text{their } 0.3)$ seen or used | M1 (1.1) | FT their $3p$; allow M1 for $(\text{their } 0.3)^2 \times (\text{their } 0.7)^{28}$
awrt $0.0018$ isw | A1 (1.1) | not from wrong working; if unsupported, allow SC1 for correct answer4 A biased octagonal dice has faces numbered from 1 to 8 . The discrete random variable $X$ is the score obtained when the dice is rolled once. The probability distribution of $X$ is shown in the table below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | }
\hline
$x$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
$\mathrm { P } ( X = x )$ & $p$ & $p$ & $p$ & $p$ & $p$ & $p$ & $p$ & $3 p$ \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Determine the value of $p$.
\item Find the probability that a score of at least 4 is obtained when the dice is rolled once.
The dice is rolled 30 times.
\item Determine the probability that a score of 8 occurs exactly twice.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2023 Q4 [5]}}