>I'm trying this test today, but surely the laws of chance are at play here?

Of course they are. But the understanding of statistics helps us to use a
small sample to examine the entire population. As long as you get a good
sized sample of bees you should get a good representation of the population
(I think you need to have a sample size of at least 40, but more is better).
For example when a blood test is done a small sample is used to count cells
and that number is used to judge the whole. I would guess that there is some
small bias as brood chamber comb will have more nurse bees than field bees,
but for finding mites that could be better.