Imagine a gun which fires N = 2m | 0 < m \in Z bullets every second with a uniformly random speed [0, 1] m/s in a single direction in a vacuum. When two bullets collide they both disappear. What is the probability of a[ny] bullet escape[ing] as time approaches infinity?
Escaping is defined as not disappearing continuing on without collision forever.
e.g. m = 1, N = 2,
Bullet 0 is fired at t=0, traveling at 0.1m/s. Bullet 1 is fired at t=1, traveling at 0.9m/s. Bullet 0 and Bullet 1 collide at time t=1.125 and both disappear. Neither bullet escapes.
| N | p |
|---|---|
| 2 | 0.5 |
| 4 | 0.625 |
| 6 | 0.69 |
| 8 | 0.72 |
| 10 | 0.75 |
python bullets.py > output.txt
python lines.py > output.txt