So, for fingerprints, have actual similarity studied been performed on a sample size large enough to draw conclusions about the test of the population?

Chance?

Hashes are not unique by definition, though we can treat them as such in many practical situations. The same is true for anything with a fixed number of variables with finite states, e.g. DNA.

There's a 1 in 2^46 chance that siblings born separately will have mostly identical DNA, minus a few random mutations.

The DNA usually isn’t completely sequenced. Instead, they look at specific regions of the genome called short tandem repeats, or STRs. Each STR consists of a short pattern of a few bases that repeats over and over. The theory is that individuals have different numbers of repeats—you might have ten repeats of AATG at the TPOX locus, while I only have nine. Individually, this doesn’t tell you much, but if you combine information from multiple loci—six repeats there, seven here, and four there-you can rapidly find profiles that are unlikely to belong to more than one person. This works best if the set are statistically independent.

Still, one can be (un)lucky, or the statistical models could be wrong—maybe the number of repeats is different in a sub population or the STRs aren’tstatistically independent.