OCR MEI D1 2011 January — Question 5 16 marks

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2011
SessionJanuary
Marks16
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPermutations & Arrangements
TypeOptimization assignment problems
DifficultyModerate -0.8 This is a standard D1 simulation question requiring students to assign random number ranges to probabilities and execute a simple simulation. The probability conversions are straightforward (converting fractions to cumulative probabilities), and the execution is mechanical with no problem-solving insight required. While it has multiple parts, each is routine application of textbook simulation techniques, making it easier than average for A-level.
5 Viola and Orsino are arguing about which striker to include in their fantasy football team. Viola prefers Rocinate, who creates lots of goal chances, but is less good at converting them into goals. Orsino prefers Quince, who is not so good at creating goal chances, but who is better at converting them into goals. The information for Rocinate and Quince is shown in the tables.
\multirow{2}{*}{}Number of chances created per match
RocinateQuince
Number67895678
Probability\(\frac { 1 } { 20 }\)\(\frac { 1 } { 4 }\)\(\frac { 1 } { 2 }\)\(\frac { 1 } { 5 }\)\(\frac { 1 } { 3 }\)\(\frac { 1 } { 3 }\)\(\frac { 1 } { 6 }\)\(\frac { 1 } { 6 }\)
Probability of converting a chance into a goal
RocinateQuince
0.10.12
  1. Give an efficient rule for using 2-digit random numbers to simulate the number of chances created by Rocinate in a match.
  2. Give a rule for using 2-digit random numbers to simulate the conversion of chances into goals by Rocinate.
  3. Your Printed Answer Book shows the result of simulating the number of goals scored by Rocinate in nine matches. Use the random numbers given to complete the tenth simulation, showing which of your simulated chances are converted into goals.
  4. Give an efficient rule for using 2-digit random numbers to simulate the number of chances created by Quince in a match.
  5. Your Printed Answer Book shows the result of simulating the number of goals scored by Quince in nine matches. Use the random numbers given to complete the tenth simulation, showing which of your simulated chances are converted into goals.
  6. Which striker, if any, is favoured by the simulation? Justify your answer.
  7. How could the reliability of the simulation be improved?
Question 5:
Part (i)
AnswerMarks Guidance
AnswerMarks Guidance
Rule using 2-digit numbers, e.g. 00–04→6, 05–29→7, 30–79→8, 80–99→9M1 rule using 2-digit nos
Correct proportionsA1
Efficient ruleA1
Part (ii)
AnswerMarks Guidance
AnswerMarks Guidance
e.g. 00–09→goal, 10–99→no goalB1 complete rule required
Part (iii)
AnswerMarks Guidance
AnswerMarks Guidance
Starting number (e.g. 8) identified from rule (i)B1 \(\sqrt{}\) rule (i)
Correct random numbers listed (e.g. 0,1,0,0,0,0,0,0)B1 \(\sqrt{}\) need to see which are converted using their 8 and rule (ii)
Conclusion: 1 goalB1 \(\sqrt{}\) their 8 and rule (ii) ... ignore previous line
Part (iv)
AnswerMarks Guidance
AnswerMarks Guidance
2 or more values rejected, e.g. 00–31→5, 32–63→6, 64–79→7, 80–95→8, 96–99 reject and redrawM1 allow part (iv) if seen elsewhere; 3 or 4 rejected
Correct proportionsA1
EfficientA1
Part (v)
AnswerMarks Guidance
AnswerMarks Guidance
Starting number (e.g. 6) from rule (iv)B1 \(\sqrt{}\) rule (iv)
Correct random numbers appliedM1 \(\sqrt{}\) their 6 ... need to see which are converted
Conclusion: 1 goalA1 \(\sqrt{}\)
Part (vi)
AnswerMarks Guidance
AnswerMarks Guidance
Each scored 10 goals; nothing to choose between themM1 goals scored
A1one, the other or indifferent, depending on goals scored
Part (vii)
AnswerMarks Guidance
AnswerMarks Guidance
More repetitionsB1 "greater number of random numbers" \(\to 0\); "more accurate data" \(\to 0\); also no "or"s; 3-digit RNs \(\to 0\) 
# Question 5:

## Part (i)

| Answer | Marks | Guidance |
|--------|-------|----------|
| Rule using 2-digit numbers, e.g. 00–04→6, 05–29→7, 30–79→8, 80–99→9 | M1 | rule using 2-digit nos |
| Correct proportions | A1 | |
| Efficient rule | A1 | |

## Part (ii)

| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. 00–09→goal, 10–99→no goal | B1 | complete rule required |

## Part (iii)

| Answer | Marks | Guidance |
|--------|-------|----------|
| Starting number (e.g. 8) identified from rule (i) | B1 | $\sqrt{}$ rule (i) |
| Correct random numbers listed (e.g. 0,1,0,0,0,0,0,0) | B1 | $\sqrt{}$ need to see which are converted using their 8 and rule (ii) |
| Conclusion: 1 goal | B1 | $\sqrt{}$ their 8 and rule (ii) ... ignore previous line |

## Part (iv)

| Answer | Marks | Guidance |
|--------|-------|----------|
| 2 or more values rejected, e.g. 00–31→5, 32–63→6, 64–79→7, 80–95→8, 96–99 reject and redraw | M1 | allow part (iv) if seen elsewhere; 3 or 4 rejected |
| Correct proportions | A1 | |
| Efficient | A1 | |

## Part (v)

| Answer | Marks | Guidance |
|--------|-------|----------|
| Starting number (e.g. 6) from rule (iv) | B1 | $\sqrt{}$ rule (iv) |
| Correct random numbers applied | M1 | $\sqrt{}$ their 6 ... need to see which are converted |
| Conclusion: 1 goal | A1 | $\sqrt{}$ |

## Part (vi)

| Answer | Marks | Guidance |
|--------|-------|----------|
| Each scored 10 goals; nothing to choose between them | M1 | goals scored |
| | A1 | one, the other or indifferent, depending on goals scored |

## Part (vii)

| Answer | Marks | Guidance |
|--------|-------|----------|
| More repetitions | B1 | "greater number of random numbers" $\to 0$; "more accurate data" $\to 0$; also no "or"s; 3-digit RNs $\to 0$ |
5 Viola and Orsino are arguing about which striker to include in their fantasy football team. Viola prefers Rocinate, who creates lots of goal chances, but is less good at converting them into goals. Orsino prefers Quince, who is not so good at creating goal chances, but who is better at converting them into goals.

The information for Rocinate and Quince is shown in the tables.

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
\multirow{2}{*}{} & \multicolumn{8}{|c|}{Number of chances created per match} \\
\hline
 & \multicolumn{4}{|c|}{Rocinate} & \multicolumn{4}{|c|}{Quince} \\
\hline
Number & 6 & 7 & 8 & 9 & 5 & 6 & 7 & 8 \\
\hline
Probability & $\frac { 1 } { 20 }$ & $\frac { 1 } { 4 }$ & $\frac { 1 } { 2 }$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 3 }$ & $\frac { 1 } { 3 }$ & $\frac { 1 } { 6 }$ & $\frac { 1 } { 6 }$ \\
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{ | c | c | }
\hline
\multicolumn{2}{|c|}{Probability of converting a chance into a goal} \\
\hline
Rocinate & Quince \\
\hline
0.1 & 0.12 \\
\hline
\end{tabular}
\end{center}

(i) Give an efficient rule for using 2-digit random numbers to simulate the number of chances created by Rocinate in a match.\\
(ii) Give a rule for using 2-digit random numbers to simulate the conversion of chances into goals by Rocinate.\\
(iii) Your Printed Answer Book shows the result of simulating the number of goals scored by Rocinate in nine matches. Use the random numbers given to complete the tenth simulation, showing which of your simulated chances are converted into goals.\\
(iv) Give an efficient rule for using 2-digit random numbers to simulate the number of chances created by Quince in a match.\\
(v) Your Printed Answer Book shows the result of simulating the number of goals scored by Quince in nine matches. Use the random numbers given to complete the tenth simulation, showing which of your simulated chances are converted into goals.\\
(vi) Which striker, if any, is favoured by the simulation? Justify your answer.\\
(vii) How could the reliability of the simulation be improved?

\hfill \mbox{\textit{OCR MEI D1 2011 Q5 [16]}}
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