| Exam Board | Edexcel |
|---|---|
| Module | FD2 (Further Decision 2) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Decision tree with EMV |
| Difficulty | Moderate -0.8 This is a straightforward decision tree construction with EMV calculation. Students need to draw three branches with two delay outcomes each, calculate probabilities (including 'no delay'), compute expected times using basic probability, and compare three values. It's mechanical application of a standard technique with no conceptual challenges or novel problem-solving required. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space |
| Transport option | Usual travel time | Possible delay time | Probability of delay |
| \multirow{2}{*}{Car} | \multirow{2}{*}{52} | 10 | 0.10 |
| 25 | 0.02 | ||
| \multirow{2}{*}{Train} | \multirow{2}{*}{45} | 15 | 0.05 |
| 25 | 0.03 | ||
| \multirow{2}{*}{Coach} | \multirow{2}{*}{55} | 5 | 0.05 |
| 15 | 0.01 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Tree diagram with correct decision node and at least three chance nodes | M1 | Tree diagram with at least nine end pay-offs, one decision node and at least three chance nodes used correctly |
| Correct structure with all arcs labelled correctly including probabilities | A1 | Correct structure of tree diagram with each arc labelled correctly |
| At least three end pay-offs consistent with stated probabilities (e.g. time 52 with probability 0.88); all nine attempted | M1 | |
| Chance nodes attempted with probabilities filled in on diagram | M1 | |
| CAO for chance and decision nodes completed correctly | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Minimum expected travel time is \(46.5\) minutes | B1ft | Correct travel time from completed tree diagram (dependent on all method marks in (a)) |
| Transport option is Train | B1 | Deduction of correct transport option; must include double line through inferior options in (a) |
# Question 3:
## Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Tree diagram with correct decision node and at least three chance nodes | M1 | Tree diagram with at least nine end pay-offs, one decision node and at least three chance nodes used correctly |
| Correct structure with all arcs labelled correctly including probabilities | A1 | Correct structure of tree diagram with each arc labelled correctly |
| At least three end pay-offs consistent with stated probabilities (e.g. time 52 with probability 0.88); all nine attempted | M1 | |
| Chance nodes attempted with probabilities filled in on diagram | M1 | |
| CAO for chance and decision nodes completed correctly | A1 | |
## Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Minimum expected travel time is $46.5$ minutes | B1ft | Correct travel time from completed tree diagram (dependent on all method marks in (a)) |
| Transport option is Train | B1 | Deduction of correct transport option; must include double line through inferior options in (a) |
---3. The table below shows the transport options, usual travel times, possible delay times and corresponding probabilities of delay for a journey. All times are in minutes.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Transport option & Usual travel time & Possible delay time & Probability of delay \\
\hline
\multirow{2}{*}{Car} & \multirow{2}{*}{52} & 10 & 0.10 \\
\hline
& & 25 & 0.02 \\
\hline
\multirow{2}{*}{Train} & \multirow{2}{*}{45} & 15 & 0.05 \\
\hline
& & 25 & 0.03 \\
\hline
\multirow{2}{*}{Coach} & \multirow{2}{*}{55} & 5 & 0.05 \\
\hline
& & 15 & 0.01 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a decision tree to model the transport options and the possible outcomes.
\item State the minimum expected travel time and the corresponding transport option indicated by the decision tree.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD2 2022 Q3 [7]}}