| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2021 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Direct binomial probability calculation |
| Difficulty | Moderate -0.8 This is a straightforward application of binomial probability formulas with n=32, p=0.4. Part (a) requires a single calculation of P(X=12), and part (b) requires P(X≥8) = 1-P(X≤7), both executable directly on a calculator. No conceptual difficulty or problem-solving insight needed—pure routine calculation below average difficulty. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0.14\), \(0.139\) or awrt \(0.1385\) isw BC | B1 | |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(X \leq 7) = 0.0248(2...)\) soi or \(0.9751\) to \(0.9752\) seen | M1 | if M0, allow SC1 for awrt \(0.0575...\) or \(0.943\); NB \(0.975178058\) |
| \(0.975\) cao | A1 | |
| [2] |
## Question 5(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.14$, $0.139$ or awrt $0.1385$ **isw BC** | B1 | |
| | **[1]** | |
---
## Question 5(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(X \leq 7) = 0.0248(2...)$ **soi** or $0.9751$ to $0.9752$ seen | M1 | if **M0**, allow **SC1** for awrt $0.0575...$ or $0.943$; **NB** $0.975178058$ |
| $0.975$ **cao** | A1 | |
| | **[2]** | |
---5 It is known that 40\% of people in Britain carry a certain gene.\\
A random sample of 32 people is collected.
\begin{enumerate}[label=(\alph*)]
\item Calculate the probability that exactly 12 people carry the gene.
\item Calculate the probability that at least 8 people carry the gene, giving your answer correct to $\mathbf { 3 }$ decimal places.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2021 Q5 [3]}}