Earlier quoted context omitted.
Currently in the US ~85% of tests turn negative. If sample turned positive you'd perform 10% more tests (1 extra test for each 10 tests) i.e. x1.1. If it turned negative you'd perform 10% the tests you'd normally perform without this scheme i.e. x0.1. In this case .85 of tests would be .1 of what they're now. The rest of .15 will be 1.1 of what they're now. So if US did this, they would be testing ~x.3 of their curre…
This isn't accounting for combinatorial math. If each sample is negative 85%, then the probability that all 10 samples are negative is 0.85^10, or about 20%. If any sample turned positive (the other 80% of the time), then all will need to be retested. Instead of 1 test per sample, you're now running 0.2 * 0.1 + 0.8 * 1.1, or about 0.9 tests per sample. You've increased throughput by 10%, but not nearly as much as was…
If you include that your goal is to test everyone too, I have no doubt that you can easily reach 96% negative test quite easily.
I remember in Quebec while we were only testing people with symptoms and that had traveled (or have been in contact with someone that has been tested positive), we were still way higher than 90% of negative tests (even right now we are a 90.1%