| Exam Board | Edexcel |
|---|---|
| Module | FD2 (Further Decision 2) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Decision tree with EMV |
| Difficulty | Moderate -0.3 This is a straightforward two-stage decision tree problem with simple probability calculations (20/52 and 8/52) and basic EMV computations. While it requires systematic organization and multiple calculations, the concepts are standard for FD2 with no novel insights needed—slightly easier than a typical A-level question due to its mechanical nature. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06c Working with constraints: algebra and ad hoc methods |
4. A game uses a standard pack of 52 playing cards.
A player gives 5 tokens to play and then picks a card. If they pick a $2,3,4,5$ or 6 then they gain 15 tokens. If any other card is picked they lose.
If they lose, the card is replaced and they can choose to pick again for another 5 tokens. This time if they pick either an ace or a king they gain 40 tokens. If any other card is picked they lose.
Daniel is deciding whether to play this game.
\begin{enumerate}[label=(\alph*)]
\item Draw a decision tree to model Daniel's possible decisions and the possible outcomes.
\item Calculate Daniel's optimal EMV and state the optimal strategy indicated by the decision tree.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD2 Q4 [8]}}