| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Conditional probability from tree |
| Difficulty | Moderate -0.8 This is a straightforward tree diagram probability question requiring basic probability rules (multiplication along branches, addition across outcomes, and conditional probability using Bayes' theorem). All three parts are standard textbook exercises with clear methods: (i) multiply probabilities, (ii) sum relevant branches, (iii) apply P(A|B) = P(A∩B)/P(B). No problem-solving insight needed, just careful arithmetic and routine application of formulas. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
Andy can walk to work, travel by bike or travel by bus. The tree diagram shows the probabilities of any day being dry or wet and the corresponding probabilities for each of Andy's methods of travel.
\includegraphics{figure_5}
A day is selected at random. Find the probability that
\begin{enumerate}[label=(\roman*)]
\item the weather is wet and Andy travels by bus, [2]
\item Andy walks or travels by bike, [3]
\item the weather is dry given that Andy walks or travels by bike. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2011 Q5 [8]}}