I am not aware of countries that test completely randomly. But many countries have so-called sentinel surveillance, where 1-5% of family doctors (general practitioners) send in samples to a lab from patients who appear with influenza-like or respiratory symptoms. This is how they monitor the spread of different kinds of influenza strain. In principle, if there’s enough testing capacity and it’s judged worthwhile, this could be expanded to also test these samples for SARS-CoV-2.
This makes it sound like at least one German state has tested for coronavirus as part of their sentinel surveillance, but I’m not sure if that test was completely random:
https://www.ecdc.europa.eu/en/seasonal-influenza/surveillanc...
This makes it sound like at least one German state has tested for coronavirus as part of their sentinel surveillance, but I’m not sure if that test was completely random:
https://twitter.com/MSI_BW/status/1233333090896039936