| Exam Board | Edexcel |
|---|---|
| Module | FD2 (Further Decision 2) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| 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 problem with clear monetary values and probabilities given explicitly. Students only need to construct a simple two-stage tree (insure/don't insure, then rain/fine), calculate two EMVs by multiplication and addition, and compare. No complex optimization, multi-stage reasoning, or novel insight required—purely mechanical application of the standard EMV algorithm taught in D2/FD2. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06c Working with constraints: algebra and ad hoc methods |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Tree diagram with decision node (9200), two chance nodes (9200 and 8000), four end pay-offs: Rain \(\rightarrow -6000\), Fine \(\rightarrow 13000\) (Insure branch); Rain \(\rightarrow -20000\), Fine \(\rightarrow 15000\) (Don't insure branch), with probabilities 0.2 and 0.8 on each branch | M1 | Tree diagram with at least four end pay-offs, one decision node and two chance nodes used correctly |
| Correct structure with arcs labelled with words and probabilities | A1 | Correct structure with each arc labelled correctly with word and associated probabilities |
| At least three end pay-offs correct including triangles | A1 | At least three end pay-offs correct including triangles; all four attempted |
| Both chance nodes completed: Insure node = 9200, Don't insure node = 8000 | M1 | Both chance nodes completed with at least one value correct |
| The theatre owner should take out the insurance | A1 | All three nodes correctly filled in on diagram + clear conclusion 'insure' including double line through inferior option |
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Tree diagram with decision node (9200), two chance nodes (9200 and 8000), four end pay-offs: Rain $\rightarrow -6000$, Fine $\rightarrow 13000$ (Insure branch); Rain $\rightarrow -20000$, Fine $\rightarrow 15000$ (Don't insure branch), with probabilities 0.2 and 0.8 on each branch | M1 | Tree diagram with at least four end pay-offs, one decision node and two chance nodes used correctly |
| Correct structure with arcs labelled with words and probabilities | A1 | Correct structure with each arc labelled correctly with word and associated probabilities |
| At least three end pay-offs correct including triangles | A1 | At least three end pay-offs correct including triangles; all four attempted |
| Both chance nodes completed: Insure node = 9200, Don't insure node = 8000 | M1 | Both chance nodes completed with at least one value correct |
| The theatre owner **should** take out the insurance | A1 | All three nodes correctly filled in on diagram + clear conclusion 'insure' including double line through inferior option |
---2. An outdoor theatre is holding a summer gala performance. The theatre owner must decide whether to take out insurance against rain for this performance.
The theatre owner estimates that
\begin{itemize}
\item on a fine day, the total profit will be $\pounds 15000$
\item on a wet day, the total loss will be $\pounds 20000$
\end{itemize}
Insurance against rain costs $\pounds 2000$. If the performance must be cancelled due to rain, then the theatre owner will receive $\pounds 16000$ from the insurer. If the performance is not cancelled due to rain, then the theatre owner will receive nothing from the insurer.
The probability of rain on the day of the gala performance is 0.2\\
Draw a decision tree and hence determine whether the theatre owner should take out the insurance against rain for this performance.\\
\hfill \mbox{\textit{Edexcel FD2 2023 Q2 [5]}}