| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Repeated trials with selection |
| Difficulty | Standard +0.3 This is a straightforward probability question involving independent trials with equal probabilities. Part (i) is basic conditional probability (1/5), part (ii) requires counting arrangements (5!/5^5), and part (iii) is simply 1 minus part (ii). While it requires careful counting in part (ii), the concepts are standard S1 material with no novel insight needed. |
| Spec | 2.03a Mutually exclusive and independent events5.01a Permutations and combinations: evaluate probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(1 \times \frac{1}{5} = \frac{1}{5}\) | M1, A1 | 2 marks |
| (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 \(1 \times \frac{4}{5} \times\) or just \(\frac{4}{5} \times\), M1 dep for fully correct product, A1 | 3 marks |
| (iii) \(1 - 0.0384 = 0.9616\) or \(601/625\) | B1 | 1 mark |
**(i)** $1 \times \frac{1}{5} = \frac{1}{5}$ | M1, A1 | 2 marks
**(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 $1 \times \frac{4}{5} \times$ or just $\frac{4}{5} \times$, M1 dep for fully correct product, A1 | 3 marks
**(iii)** $1 - 0.0384 = 0.9616$ or $601/625$ | B1 | 1 mark
**TOTAL: 6 marks**
---4 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 2010 Q4 [6]}}