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 |
| Rocinate | Quince |
| Number | 6 | 7 | 8 | 9 | 5 | 6 | 7 | 8 |
| 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 |
| Rocinate | Quince |
| 0.1 | 0.12 |
- Give an efficient rule for using 2-digit random numbers to simulate the number of chances created by Rocinate in a match.
- Give a rule for using 2-digit random numbers to simulate the conversion of chances into goals by Rocinate.
- 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.
- Give an efficient rule for using 2-digit random numbers to simulate the number of chances created by Quince in a match.
- 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.
- Which striker, if any, is favoured by the simulation? Justify your answer.
- How could the reliability of the simulation be improved?