Are the false positives IID, or are they correlated to each other in the same individual, i.e. a false positive will likely test false positive again, a true negative will likely never test false positive? This is the kind of critically important stuff in stochastic processing theory that medical-field statistics never seem to care to report on.
If it is the former (IID), and let's say P_D = 1.0, P_FA = 0.2, it is an extremely easy problem to solve: Just have each student take 3 tests each day, which will reduce the overall P_FA from 0.2 to 0.008. Or 4 tests for 0.0016.
If it is the latter, you will only lose 6 students for the whole week; you'll have 24 students left on Friday, not 10.
If it is the former (IID), and let's say P_D = 1.0, P_FA = 0.2, it is an extremely easy problem to solve: Just have each student take 3 tests each day, which will reduce the overall P_FA from 0.2 to 0.008. Or 4 tests for 0.0016.
If it is the latter, you will only lose 6 students for the whole week; you'll have 24 students left on Friday, not 10.