| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | Geometric with multiple success milestones |
| Difficulty | Moderate -0.8 This is a straightforward application of the geometric distribution with standard formulas. Part (i) requires P(X=10) = (0.95)^9 × 0.05, part (ii) is simply (0.95)^10, and part (iii) is recall of E(X) = 1/p = 20. All three parts are direct formula application with no problem-solving or conceptual challenge, making this easier than average even for Further Maths. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1) |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (i) | 0.959 × 0.05 |
| = 0.0315 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (ii) | 0.9510 = 0.599 |
| [1] | 1.1 | |
| 1 | (iii) | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 0.05 | B1 | |
| [1] | 1.1 | N |
Question 1:
1 | (i) | 0.959 × 0.05
= 0.0315 | M1
A1
[2] | 3.3
1.1
1 | (ii) | 0.9510 = 0.599 | B1
[1] | 1.1
1 | (iii) | 1
(cid:32) 20
0.05 | B1
[1] | 1.1 | NA darts player is trying to hit the bullseye on a dart board. On each throw the probability that she hits it is $0.05$, independently of any other throw.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that she hits the bullseye for the first time on her $10$th throw. [2]
\item Find the probability that she does not hit the bullseye in her first $10$ throws. [1]
\item Write down the expected number of throws which it takes her to hit the bullseye for the first time. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor Q1 [4]}}