1. ## Probability-collisions

I have to do this question as a part of my homework but I have confuse. I m not sure about the first part of this question, and i m really confuse for part iii. I have attach the spreadsheet with the simulation and the work that I have done until now. Any advice can help

Set up the simulator so that there are two routes, with a SPAD probability of 0.5 on each route. Route 1 has a random start - initially with a start probability of 1. On route 2 the signal position has been moved back to 22 so that a SPAD can only result in a collision if there is leaf mulch and the probability of leaf mulch is set to 0.5. (For this simulation, we are assuming that visibility is good).

(i) Use a tree diagram to calculate the number of collisions that would be expected in 16 train rides if train 1 always started on time (ie with "start probability" set to 1).

(ii) Set the start probability to 1 and run the simulator 5 times

After each run you should have a column of 10 numbers, each representing the number of collisions in 16 train rides. Average these and record the result. After 5 runs of the simulator you will thus have 5 averages. Perform a suitable statistical test to determine whether these are in agreement with the number you have calculated in (i)

(iii)Alter the starting aspect for train 2 to green (by typing the word green in cell W15) Set the basic spad probability and leaf mulch probabilities for route 2 to 1 (ie cells R16 and R17). Verify that you now get approx 8 collisions in 16 runs. (iii) Alter the start probability until the number of collisions halves. Give suitable evidence from your simulator results to show that the number of collisions has halved. Explain theoretically why the start probability you have found has halved the number of collisions.

(iv) Use the probability you have found in (iii) for a random start on both routes. What effect does this have on the number of collisions? Can you explain this theoretically?