4 Joe is to catch a plane to go on holiday. He has arranged to leave his car at a car park near to the airport. There is a bus service from the car park to the airport, and the bus leaves when there are at least 15 passengers on board. Joe is delayed getting to the car park and arrives needing the bus to leave within 15 minutes if he is to catch his plane. He is the \(10 ^ { \text {th } }\) passenger to board the bus, so he has to wait for another 5 passengers to arrive.
The distribution of the time intervals between car arrivals and the distribution of the number of passengers per car are given below.
| Time interval between cars (minutes) | 1 | 2 | 3 | 4 | 5 |
| Probability | \(\frac { 1 } { 10 }\) | \(\frac { 3 } { 10 }\) | \(\frac { 2 } { 5 }\) | \(\frac { 1 } { 10 }\) | \(\frac { 1 } { 10 }\) |
| Number of passengers per car | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | \(\frac { 1 } { 6 }\) | \(\frac { 1 } { 3 }\) | \(\frac { 1 } { 12 }\) | \(\frac { 1 } { 4 }\) | \(\frac { 1 } { 12 }\) | \(\frac { 1 } { 12 }\) |
- Give an efficient rule for using 2-digit random numbers to simulate the intervals between car arrivals.
- Give an efficient rule for using 2-digit random numbers to simulate the number of passengers in a car.
- The incomplete table in your answer book shows the results of nine simulations of the situation. Complete the table, showing in each case whether or not Joe catches his plane.
- Use the random numbers provided in your answer book to run a tenth simulation.
[0pt] - Estimate the probability of Joe catching his plane. State how you could improve your estimate. [2]