| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modelling and Hypothesis Testing |
| Type | Markov chain transition simulation |
| Difficulty | Easy -1.2 This is a straightforward simulation exercise requiring only basic probability interpretation and rule construction. Students must assign random number ranges proportionally (e.g., 0-3 for coffee with p=1/3) and apply them mechanically to given data. No mathematical derivation, proof, or complex reasoning is needed—just careful bookkeeping across multiple parts. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| (i) e.g. 0,1,2 → coffee; 3,4,5,6,7,8 → tea; (9 → reject and redraw) | M1, A1 | reject proportions + efficient, ie using 9 digits (so allow 00, 01, ..., 09) |
| (ii) Ten simulated coffees or teas, corresponding to their rule and the given random digits. e.g. T C C T C T T C T C; e.g. C T T T C T T C T | B1 | |
| (iii) e.g. Coffee at breakfast: 00-54 → coffee; 55-99 → tea; Tea at breakfast: 00-14 → tea; 15-99 → coffee | B1, B1 | Breakfast drink must be specified. (for each) |
| (iv) Ten simulated coffees or teas, using answers to part (ii) to define which rule to use. e.g. C C T C C C C T C; e.g. C C T C C T C C C C; e.g. C C C C T T C C C T | M1, A1 | first 4, ref part (ii) ft errors in (ii) |
| (v) Accumulating and computing the proportion. e.g. C - 65% | B1 | ft |
**(i)** e.g. 0,1,2 → coffee; 3,4,5,6,7,8 → tea; (9 → reject and redraw) | M1, A1 | reject proportions + efficient, ie using 9 digits (so allow 00, 01, ..., 09)
**(ii)** Ten simulated coffees or teas, corresponding to their rule and the given random digits. e.g. T C C T C T T C T C; e.g. C T T T C T T C T | B1 |
**(iii)** e.g. Coffee at breakfast: 00-54 → coffee; 55-99 → tea; Tea at breakfast: 00-14 → tea; 15-99 → coffee | B1, B1 | Breakfast drink must be specified. (for each)
**(iv)** Ten simulated coffees or teas, using answers to part (ii) to define which rule to use. e.g. C C T C C C C T C; e.g. C C T C C T C C C C; e.g. C C C C T T C C C T | M1, A1 | first 4, ref part (ii) ft errors in (ii)
**(v)** Accumulating and computing the proportion. e.g. C - 65% | B1 | ft2 Honor either has coffee or tea at breakfast. On one third of days she chooses coffee, otherwise she has tea. She can never remember what she had the day before.\\
(i) Construct a simulation rule, using one-digit random numbers, to model Honor's choices of breakfast drink.\\
(ii) Using the one-digit random numbers in your answer book, simulate Honor's choice of breakfast drink for 10 days.
Honor also has either coffee or tea at the end of her evening meal, but she does remember what she had for breakfast, and her choice depends on it. If she had coffee at breakfast then the probability of her having coffee again is 0.55 . If she had tea for breakfast, then the probability of her having tea again is 0.15 .\\
(iii) Construct a simulation rule, using two-digit random numbers, to model Honor's choice of evening drink given that she had coffee at breakfast.
Construct a simulation rule, using two-digit random numbers, to model Honor's choice of evening drink given that she had tea at breakfast.\\
(iv) Using your breakfast simulation from part (ii), and the two-digit random numbers in your answer book, simulate Honor's choice of evening drink for 10 days.\\
(v) Use your results from parts (ii) and (iv) to estimate the proportion of Honor's drinks, breakfast and evening meal combined, which are coffee.
\section*{Question 3 begins on page 4}
\hfill \mbox{\textit{OCR MEI D1 2014 Q2 [8]}}