Picking two random points in space and drawing a line between them, what is the chance the line intersects anything? I thought of this question after pondering how most of the observable universe is observable. If we can observe it, then the space between us and that object must have been unoccupied to allow the photons to travel uninterrupted.
Indeed this is correct.  Photons can travel distances greater than the radius of the observable universe without interacting with matter.  This has been true ever since the period know as &quot;recombination&quot; when electrons became bound to hydrogen and helium nuclei.  Prior to that time there were lots of free electrons that could interact with light.  After that time the electrons became bound to protons, and the electrically neutral gas was effectively transparent.  We can still see the photons emitted at that time, although now they have been cooled by the expansion of the universe and appear in the microwave part of the radio spectrum (This is called the cosmic microwave background)
Now the matter in the universe is concentrated into galaxies within galaxies it is consentrated into stars,  so the mean free path of photons in the universe is still much larger than the scale of the universe.
The region that is very distant is also very far back in time, and before recombination we can't &quot;see&quot; because the universe was &quot;foggy&quot; because of the free electrons.  Most of what we know about the universe before this time is inferred from observations of how matter behaves at high energies,