I really don't like this math, no one actually stops at that point, you take the output, la, "0.9005" and re-run it

     (0.9005 × .1) × (1-.995) + (0.9005 × .9)

and again, and again, etc, point being that over time it does cycle the entire room, due to entropy, and then suddenly the differences start to stack up a bit, not a lot, but when one filter is letting 10x the particles through vs the other filter, it'll show