| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Conditional probability tree diagram |
| Difficulty | Standard +0.3 This is a straightforward conditional probability tree diagram problem with clear state transitions. While it requires careful bookkeeping across multiple stages (up to 5 sets total), the probabilities are given explicitly, the tree structure is standard, and the calculations involve only multiplication and addition of probabilities along branches. Slightly easier than average due to the mechanical nature of the task. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
3 Jimmy and Alan are playing a tennis match against each other. The winner of the match is the first player to win three sets. Jimmy won the first set and Alan won the second set. For each of the remaining sets, the probability that Jimmy wins a set is
\begin{itemize}
\item 0.7 if he won the previous set,
\item 0.4 if Alan won the previous set.
\end{itemize}
It is not possible to draw a set.\\
(i) Draw a probability tree diagram to illustrate the possible outcomes for each of the remaining sets.\\
(ii) Find the probability that Alan wins the match.\\
(iii) Find the probability that the match ends after exactly four sets have been played.
\hfill \mbox{\textit{OCR MEI S1 2012 Q3 [8]}}