| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Listing outcomes and counting |
| Difficulty | Moderate -0.3 This is a straightforward probability question requiring systematic listing of outcomes and basic probability calculations. Part (i) tests basic comprehension, part (ii) requires careful enumeration (not difficult but requires attention), and part (iii) involves multiplying probabilities along branches—all standard S1 techniques with no novel problem-solving required. Slightly easier than average due to the structured guidance and limited complexity. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks |
|---|---|
| Impossible because the competition would have finished as soon as Sophie had won the first 2 matches | E1 |
| TOTAL: 1 |
| Answer | Marks |
|---|---|
| SS, JSS, SJSS | B1, B1, B1 (-1 each error or omission) |
| TOTAL: 3 |
| Answer | Marks |
|---|---|
| \(0.7^2 + 0.3 \times 0.7^2 + 0.7 \times 0.3 \times 0.7^2 = 0.7399\) or \(0.74(0)\) | M1 for any correct term; M1 for any other correct term; M1 for sum of all three correct terms; A1 cao |
| \(\{0.49 + 0.147 + 0.1029 = 0.7399\}\) | |
| TOTAL: 4 |
## Q5(i)
Impossible because the competition would have finished as soon as Sophie had won the first 2 matches | E1 |
| TOTAL: 1 |
## Q5(ii)
SS, JSS, SJSS | B1, B1, B1 (-1 each error or omission) |
| TOTAL: 3 |
## Q5(iii)
$0.7^2 + 0.3 \times 0.7^2 + 0.7 \times 0.3 \times 0.7^2 = 0.7399$ or $0.74(0)$ | M1 for any correct term; M1 for any other correct term; M1 for sum of all three correct terms; A1 cao |
$\{0.49 + 0.147 + 0.1029 = 0.7399\}$ | |
| TOTAL: 4 |
---5 Sophie and James are having a tennis competition. The winner of the competition is the first to win 2 matches in a row. If the competition has not been decided after 5 matches, then the player who has won more matches is declared the winner of the competition.
For example, the following sequences are two ways in which Sophie could win the competition. (S represents a match won by Sophie; $\mathbf { J }$ represents a match won by James.)
\section*{SJSS SJSJS}
(i) Explain why the sequence $\mathbf { S S J }$ is not possible.\\
(ii) Write down the other three possible sequences in which Sophie wins the competition.\\
(iii) The probability that Sophie wins a match is 0.7 . Find the probability that she wins the competition in no more than 4 matches.
\hfill \mbox{\textit{OCR MEI S1 2008 Q5 [8]}}