| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Single batch expected count |
| Difficulty | Easy -1.2 This is a straightforward binomial probability question requiring only direct application of the formula P(X=0) = (0.75)^6 and then multiplication by 50 for the expectation. Both parts are routine calculations with no problem-solving or conceptual challenge beyond recognizing the binomial model. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks |
|---|---|
| Marks: M1 for \(0.75^6\), A1 CAO | 2 |
| Answer | Marks |
|---|---|
| Marks: M1 for product, A1 FT | 2 |
## (i)
**Answer/Working:** $P(X = 0) = 0.75^6 = 0.178$
**Marks:** M1 for $0.75^6$, A1 CAO | 2
**Guidance:** Or from tables 0.1780 Or 729/4096. Allow 0.18 with working
## (ii)
**Answer/Working:** $E(X) = np = 50 \times 0.178 = 8.9$
**Marks:** M1 for product, A1 FT | 2
**Guidance:** FT their answer to (i) providing it's a probability. NB A0 if subsequently rounded
---25% of the plants of a particular species have red flowers. A random sample of 6 plants is selected.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that there are no plants with red flowers in the sample. [2]
\item If 50 random samples of 6 plants are selected, find the expected number of samples in which there are no plants with red flowers. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2011 Q3 [4]}}