I believe your calculation was 70% chance of not having it given a negative test, so if you have two independent negative tests, that would be 91% chance of not having it (1 − 0.09), or 9% chance of having it. But in reality, false negatives are very common. And you need to start with a prior probability to update from. From the paper I referenced, if you have some symptoms and were exposed, the prior probability of having COVID might be 91%, but after one negative result, you are still at 77-80% probability of having COVID. However, if your symptoms don’t match the common ones for COVID or if you don’t know you were exposed, then the prior probability of having COVID is much lower to start with. Then a negative test result would update downward slightly from that prior.
Why would there be a 91% change you have covid if two (statistically) independent tests say you DON’T have it?
I believe your calculation was 70% chance of not having it given a negative test, so if you have two independent negative tests, that would be 91% chance of not having it (1 − 0.09), or 9% chance of having it. But in reality, false negatives are very common. And you need to start with a prior probability to update from. From the paper I referenced, if you have some symptoms and were exposed, the prior probability of having COVID might be 91%, but after one negative result, you are still at 77-80% probability of having COVID. However, if your symptoms don’t match the common ones for COVID or if you don’t know you were exposed, then the prior probability of having COVID is much lower to start with. Then a negative test result would update downward slightly from that prior.