Let’s consider a perfect sphere the size of the earth (500 trillion m^2). On that sphere, there are 10 racecars (each 10 m^2) going lethally fast. What are the chances they will hit each other?
Well, this depends a lot on initial conditions, but if we simply randomize their placement, it should be something on the order of the area of all the cars divided by the area of the sphere. Safe!
Now, let’s assume there are 10000 lethally fast racecars zooming around this earth-sized sphere. Now it is a bit more nerve wracking, but earth is big. And, we can assume they have good initial conditions— all in different lanes (and, IRL, mostly on different spheres!).
So, let’s make things harder. Say I have a gun that shoots 100,000 bullets in all directions on this empty earth, and those bullets keep flying around forever—how long will it take before they hit one of my 10,000 racecars? This is harder to estimate, but it should still be on the order of a 1 in 10 billion chance per orbital cycle (say, of 1 hour each?). So, in 10000 hours (~400 days), you have a chance of 1 in 1 million chance that one of the racecars will be hit by the bullets. So, it will be about a thousand years before you get to a 1 in 1000 chance. Is that about right? Don’t trust my math.
In contrast, the lifetime odds of dying in a car crash are about 1 in 100 (See cite) https://injuryfacts.nsc.org/all-injuries/preventable-death-o...