| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2022 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Conditional or compound probability scenarios |
| Difficulty | Standard +0.8 Part (a) is straightforward probability with a discrete uniform distribution. Part (b) requires recognizing a negative binomial scenario, carefully defining the sample space (stopping at the second success where success = number < 9), and computing P(N≤4) which involves multiple cases and conditional reasoning. This goes beyond routine application and requires careful probabilistic thinking about stopping times. |
| Spec | 5.02e Discrete uniform distribution5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1) |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | k−9 |
| Answer | Marks |
|---|---|
| 9 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1a |
| 1.1 | Allow M1 for numerator k – 10 or answer |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | Probability of 1 card1 be−ing𝑘𝑘 less than 9 = 0.4 |
| Answer | Marks |
|---|---|
| 625 | B1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | For 0.4 or 0.6 seen 1 − 𝑘𝑘 |
Question 4:
4 | (a) | k−9
P(X ≥10)= or
k
9 | M1
A1
[2] | 3.1a
1.1 | Allow M1 for numerator k – 10 or answer
10
4 | (b) | Probability of 1 card1 be−ing𝑘𝑘 less than 9 = 0.4
0.42 + 2 × 0.42 × 0.6 + 3 × 0.42 × 0.62
328
= 0.5248 or
625 | B1
M1
A1
[3] | 3.1a
1.1
1.1 | For 0.4 or 0.6 seen 1 − 𝑘𝑘
Allow with their 0.4 and 0.6. Allow one coefficient incorrect.
OR using X ~ B(4, 0.6) OR using X ~ B(4, 0.4)
P(X ≤ 2) = 0.5248 1 – P(X ≤ 1)= 0.52484 A pack of $k$ cards is labelled $1,2 , \ldots , k$. A card is drawn at random from the pack. The random variable $X$ represents the number on the card.
\begin{enumerate}[label=(\alph*)]
\item Given that $k > 10$, find $\mathrm { P } ( X \geqslant 10 )$.
You are now given that $k = 20$.
\item A card is drawn at random from the pack and the number on it is noted. The card is then returned to the pack. This process is repeated until the second occasion on which the number noted is less than 9 .
Find the probability that no more than 4 cards have to be drawn.
Answer all the questions.
Section B (95 marks)
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2022 Q4 [5]}}