| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Distribution |
| Type | r-th success on trial n |
| Difficulty | Moderate -0.8 This is a straightforward application of geometric and negative binomial distribution formulas. Part (a) requires a simple calculation of (0.7)²(0.3), while part (b) uses the standard formula for r-th success on n-th trial. Both are direct recall questions with minimal problem-solving, making this easier than average but not trivial since it requires recognizing the correct distribution. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1)5.02h Geometric: mean 1/p and variance (1-p)/p^2 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | 0.72×0.3 |
| = 0.147 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 3.3 | |
| 1.1 | Use of Geo(0.3) | |
| 4 | (b) | Use B(9, 0.3) to get 0.2668... |
| Answer | Marks |
|---|---|
| = 0.080(048…) | B1 |
| Answer | Marks |
|---|---|
| [3] | 2.2a |
| Answer | Marks |
|---|---|
| 1.1 | Use of correct binomial distribution |
| Answer | Marks |
|---|---|
| BC | Value may be implied |
Question 4:
4 | (a) | 0.72×0.3
= 0.147 | M1
A1
[2] | 3.3
1.1 | Use of Geo(0.3)
4 | (b) | Use B(9, 0.3) to get 0.2668...
0.2668... × 0.3
= 0.080(048…) | B1
M1
A1
[3] | 2.2a
3.1a
1.1 | Use of correct binomial distribution
Require P(3 in first 9 then also 10th)
BC | Value may be implied
0.08 scores A0
(only 1sf)4 Alex is practising bowling at a cricket wicket. Every time she bowls a ball, she has a $30 \%$ chance of hitting the wicket.
\begin{enumerate}[label=(\alph*)]
\item Assuming that successive bowls are independent, determine the probability that Alex first hits the wicket on her third attempt.
\item Determine the probability that Alex hits the wicket for the fourth time on her tenth attempt.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2022 Q4 [5]}}