This is even more terrifying when one considers the possibility that the result of the second test is not independent from the result of the first. That is, so

This is even more terrifying when one considers the possibility that the result of the second test is not independent from the result of the first. That is, some trait within the population increases the probability of a false positive (and this is likely in any heterogeneous population). Now the conditional probability of infection, given TWO positive tests is still far below 50%. This is why a second test of a different type, even if it is less accurate, if it is more likely to be independent, is much preferred!