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But how do they figure that without having visited those stars and systems they might support?
You're asking me to go back about 20 years or so (and remember that alcohol was being imbibed by most everyone during these conversations) but I'll give it a shot.
Star density does vary and that variance is based on many factors including the age of the galaxy, the type of galaxy, the size of the galaxy and so on. Astronomers used to basically "guess" how many galaxys existed beyond the comparatively small area which ground-based telescopes could observe based on the observations they could make. The Hubble telescope, which just might be the second greatest astronomical invention (after Galileo's original telescope). The Hubble has actually let us peer far further into space than ever before (and, at the same time, further back in time than ever before) so we can finally do more than guess.
Wander over to NASA's website and take a look at some of the photos of galaxies Hubble has taken- not the ones of them in 'our neighborhood (like Andromeda) but the clusters visible tens of millions of light years away from us. It's staggering how many galaxies, each with tens of not hundreds of millions of stars, are visible in some of them.
Now I'm the first to admit that the numbers I threw out are purely speculatory. Only God knws how accurate they are and He ain't telling (at least not me anyway). But there are probabilities in Statistics which say that, once the
possibility of something reaches a certain point, it becomes a
probability and a probability can, at a point, become a near-certainty. It's all mathematical, but it really requires no great understanding of meth to accept.
Think of it this way: we know that some people have red hair. If enough people walk through a particular doorway, and those people are a truly random sample of the population at large, statistically it is certain that, eventually, someone with red hair will walk through that doorway.