I don't know much about statistics, but I can add that the time period matters. If we only started observing space yesterday, and saw it, it would be weird to say "it's rare", but we've been observing space for, I don't know, up to 400 years? (counting since invention of telescope, 1608)
This type of object could only really have been seen when it was. It was picked up as part of a full-sky survey that year, the firsts time such a thing had been done at sufficient resolution to detect an object like 'Oumuamua.
A number that I saw quoted earlier was that it is expected that around 3 of these things go through the solar system every day. This one just happened to be the one caught by the survey, which itself required a bunch of coincidences since it means catching multiple pictures of the same object in different locations so as to establish a trajectory, so an ability to detect is not just resolution, but also timing and orbital trajectory.
> but we've been observing space for, I don't know, up to 400 years? (counting since invention of telescope, 1608)
We've been observing space 'forever'. Pre-telescope observers had quite accurate star maps (of the naked-eye stars, obviously) and were fully aware of the complex movements of the planets. Their models of the movements were good enough for predictions even if the underlying explanatory causal models were sometimes wrong.
