| Exam Board | OCR MEI |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modelling and Hypothesis Testing |
| Type | Marketing and operational strategy decisions |
| Difficulty | Moderate -0.5 This is a straightforward decision tree problem requiring systematic calculation of expected values across different scenarios. While it involves multiple branches and conditional probabilities, the mathematical operations are basic (percentages and weighted averages), and the tree structure follows a standard template with no novel problem-solving insight required. The Bayesian updating aspect in part (iii) is mechanical rather than conceptually challenging. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Revise D, D worth 60: \(0.8 \times 60 + 0.5 \times 40 = 48 + 20 = 68\) | B1 | |
| Revise D, S worth 60: \(0.8 \times 40 + 0.5 \times 60 = 32 + 30 = 62\) | B1 | |
| Revise S, S worth 60: \(0.7 \times 60 + 0.6 \times 40 = 42 + 24 = 66\) | B1 | |
| Revise S, D worth 60: \(0.7 \times 40 + 0.6 \times 60 = 28 + 36 = 64\) | B1 | |
| Expected mark revising D: \(0.5 \times 68 + 0.5 \times 62 = 65\) | A1 | |
| Expected mark revising S: \(0.5 \times 66 + 0.5 \times 64 = 65\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Decision node at start with branches D and S | B1 | |
| Chance nodes after each decision with 0.5/0.5 branches | B1 | |
| Correct outcomes (68, 62, 66, 64) at terminals | B1 | |
| Expected values 65, 65 shown; correct conclusion | B2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Chance node: Michael forecasts D worth 60 (prob 0.5), S worth 60 (prob 0.5) | B1 | |
| If forecast D worth 60: prob 0.7 correct, 0.3 incorrect | B1 | |
| If forecast S worth 60: prob 0.7 correct, 0.3 incorrect | B1 | |
| Correct expected marks computed at each terminal using optimal revision choice | M1 | |
| Overall expected mark with Michael's advice calculated correctly | A1 | |
| Worth of advice = improvement over 65 stated | A1 |
# Question 2:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Revise D, D worth 60: $0.8 \times 60 + 0.5 \times 40 = 48 + 20 = 68$ | B1 | |
| Revise D, S worth 60: $0.8 \times 40 + 0.5 \times 60 = 32 + 30 = 62$ | B1 | |
| Revise S, S worth 60: $0.7 \times 60 + 0.6 \times 40 = 42 + 24 = 66$ | B1 | |
| Revise S, D worth 60: $0.7 \times 40 + 0.6 \times 60 = 28 + 36 = 64$ | B1 | |
| Expected mark revising D: $0.5 \times 68 + 0.5 \times 62 = 65$ | A1 | |
| Expected mark revising S: $0.5 \times 66 + 0.5 \times 64 = 65$ | A1 | cao |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Decision node at start with branches D and S | B1 | |
| Chance nodes after each decision with 0.5/0.5 branches | B1 | |
| Correct outcomes (68, 62, 66, 64) at terminals | B1 | |
| Expected values 65, 65 shown; correct conclusion | B2 | |
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Chance node: Michael forecasts D worth 60 (prob 0.5), S worth 60 (prob 0.5) | B1 | |
| If forecast D worth 60: prob 0.7 correct, 0.3 incorrect | B1 | |
| If forecast S worth 60: prob 0.7 correct, 0.3 incorrect | B1 | |
| Correct expected marks computed at each terminal using optimal revision choice | M1 | |
| Overall expected mark with Michael's advice calculated correctly | A1 | |
| Worth of advice = improvement over 65 stated | A1 | |
---2 Zoe is preparing for a Decision Maths test on two topics, Decision Analysis (D) and Simplex (S). She has to decide whether to devote her final revision session to D or to S .
There will be two questions in the test, one on D and one on S . One will be worth 60 marks and the other will be worth 40 marks. Historically there is a 50\% chance of each possibility.
Zoe is better at $D$ than at $S$. If her final revision session is on $D$ then she would expect to score $80 \%$ of the $D$ marks and $50 \%$ of the $S$ marks. If her final session is on $S$ then she would expect to score $70 \%$ of the S marks and $60 \%$ of the D marks.\\
(i) Compute Zoe's expected mark under each of the four possible circumstances, i.e. Zoe revising $D$ and the D question being worth 60 marks, etc.\\
(ii) Draw a decision tree for Zoe.
Michael claims some expertise in forecasting which question will be worth 60 marks. When he forecasts that it will be the D question which is worth 60 , then there is a $70 \%$ chance that the D question will be worth 60 . Similarly, when he forecasts that it will be the S question which is worth 60 , then there is a $70 \%$ chance that the S question will be worth 60 . He is equally likely to forecast that the D or the S question will be worth 60.\\
(iii) Draw a decision tree to find the worth to Zoe of Michael's advice.
\hfill \mbox{\textit{OCR MEI D2 2009 Q2 [16]}}