Earlier quoted context omitted.
Sure, but a person who goes to the store 7 times a week is ~7 times as likely to have been sampled compared to someone who goes only once a week. They are also ~7 times as likely to have contracted covid-19 at the grocery store. It's likely that they are also, in general, isolating less than the other. This sampling would have a (possibly slight, but still unknown) bias towards people who are isolating less (who you…
going 7 times doesn’t actually increase the likelihood 7x but your point still stands that they would be far more likely to get it
f(N, P): (1 - ((1-P)^N)) / P
For a large P you're right, but as P gets very small (let's say that in any given trip you have a 0.01% chance of being sampled) then the increase in likelihood of being sampled approaches N times as much (in this example, it would be 6.999 times as likely). Of course, this assumes they're taking measures to ensure no one gets sampled twice.