| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2017 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Find unknown probability parameter |
| Difficulty | Moderate -0.3 This is a standard S1 tree diagram question requiring systematic application of probability rules (multiplication along branches, addition across paths) and conditional probability. While it has multiple parts and requires careful bookkeeping, the techniques are routine for this topic with no novel problem-solving insight needed. Slightly easier than average due to the structured, step-by-step nature. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03d Calculate conditional probability: from first principles |
4.The partially completed tree diagram,where $p$ and $q$ are probabilities,gives information about Andrew's journey to work each day.\\
\includegraphics[max width=\textwidth, alt={}, center]{7d45bacd-20ac-49b4-8f3f-613edf3739f9-12_661_794_395_511}\\
$R$ represents the event that it is raining\\
W represents the event that Andrew walks to work\\
$B$ represents the event that Andrew takes the bus to work\\
$C$ represents the event that Andrew cycles to work
Given that $\mathrm { P } ( B ) = 0.26$
\begin{enumerate}[label=(\alph*)]
\item find the value of $p$
Given also that $\mathrm { P } \left( R ^ { \prime } \mid W \right) = 0.175$
\item find the value of $q$
\item Find the probability that Andrew cycles to work.
Given that Andrew did not cycle to work on Friday,
\item find the probability that it was raining on Friday.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2017 Q4 [12]}}