| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Listing outcomes and counting |
| Difficulty | Standard +0.8 This question requires systematic enumeration of sequences with constraints, careful logical reasoning about termination conditions, and probability calculations across multiple pathways. The conceptual challenge of understanding when sequences terminate (part i) and ensuring complete enumeration (part ii) combined with multi-step probability calculations elevates this above standard counting exercises. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Impossible because the competition would have finished as soon as Sophie had won the first 2 matches | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| SS, JSS, JSJSS | B1, B1, B1 | \(-1\) each error or omission |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(0.7^2 + 0.3 \times 0.7^2 + 0.7 \times 0.3 \times 0.7^2 = 0.7399\) or \(0.74(0)\) | M1 | for any correct term |
| \(\{0.49 + 0.147 + 0.1029 = 0.7399\}\) | M1 | for any other correct term |
| M1 | for sum of all three correct terms | |
| A1 | cao |
## Question 3:
### Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Impossible because the competition would have finished as soon as Sophie had won the first 2 matches | E1 | |
### Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| SS, JSS, JSJSS | B1, B1, B1 | $-1$ each error or omission |
### Part (iii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $0.7^2 + 0.3 \times 0.7^2 + 0.7 \times 0.3 \times 0.7^2 = 0.7399$ or $0.74(0)$ | M1 | for any correct term |
| $\{0.49 + 0.147 + 0.1029 = 0.7399\}$ | M1 | for any other correct term |
| | M1 | for sum of all three correct terms |
| | A1 | cao |
---3 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. ( $\mathbf { S }$ 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 Q3 [8]}}