| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Multiple independent trials |
| Difficulty | Standard +0.8 This is a multi-part probability question requiring careful reasoning about dependent events and the complement rule. Part (i) is straightforward (1/5), but part (ii) requires recognizing this as a permutation problem (5!/5^5) which is non-trivial for A-level students. Part (iii) tests understanding of complements. The question demands more problem-solving insight than routine probability exercises, placing it moderately above average difficulty. |
| Spec | 2.03a Mutually exclusive and independent events |
| Answer | Marks | Guidance |
|---|---|---|
| \(1 \times \frac{1}{5} = \frac{1}{5}\) | M1, A1 | 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(1 \times \frac{4}{5} \times \frac{3}{5} \times \frac{2}{5} \times \frac{1}{5} = \frac{24}{625} = 0.0384\) | M1 for \(1 \times \frac{4}{5}\) or just \(\frac{4}{5} \times\); M1 dep for fully correct product; A1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(1 - 0.0384 = 0.9616\) or \(\frac{601}{625}\) | B1 | 1 mark |
## Question 2:
### Part (i)
$1 \times \frac{1}{5} = \frac{1}{5}$ | M1, A1 | **2 marks**
### Part (ii)
$1 \times \frac{4}{5} \times \frac{3}{5} \times \frac{2}{5} \times \frac{1}{5} = \frac{24}{625} = 0.0384$ | M1 for $1 \times \frac{4}{5}$ or just $\frac{4}{5} \times$; M1 dep for fully correct product; A1 | **3 marks**
### Part (iii)
$1 - 0.0384 = 0.9616$ or $\frac{601}{625}$ | B1 | **1 mark**
---2 Each packet of Cruncho cereal contains one free fridge magnet. There are five different types of fridge magnet to collect. They are distributed, with equal probability, randomly and independently in the packets. Keith is about to start collecting these fridge magnets.\\
(i) Find the probability that the first 2 packets that Keith buys contain the same type of fridge magnet.\\
(ii) Find the probability that Keith collects all five types of fridge magnet by buying just 5 packets.\\
(iii) Hence find the probability that Keith has to buy more than 5 packets to acquire a complete set.
\hfill \mbox{\textit{OCR MEI S1 Q2 [6]}}