Science works on probabilities all the time, though those probabilities should usually be informed by evidence. Quantum mechanics is nothing but probabilities lol.
The cosmological principle is a good example of something driven by statistics and reasoning: " the cosmological principle is the working assumption that observers on Earth do not occupy a restrictive, unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics."
It certainly could be shown to be incorrect, but is the more reasonable to start with the assumption you aren't unique or special in some way.
The earth certainly could be unique out of the 10^22 solar systems in the observable universe (ignoring the part of the universe we can't observe), but that's like balancing on the thin edge of a knife, that doesn't happen in nature. You expect there to either be zero, or plenty.
EDIT: Entropy is another thing which is statistical in nature. Entropy increases because of the number of probable states (or something like that, it's been a while).
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