Can I check something with the experts on here?
On another thread, someone asked what the probability was of 4 LFT tests being negative (if someone was actually positive).
My calculation, taking the % of false negatives as around 50% (optimistic in real life usage for asymptomatic cases, but easy to work with), was that this was 1/16 (1 divided by 2 to the power 4).
Then the probability of 'being positive with 4 false negatives' overall was (1/16) * (1/560) (current prevalence of positive cases from ONS).
Obvious caveats are that if those 4 LFTs are taken at intervals over a period, and if you were infected at the start of the period of testing, the false negative probability would go down (because viral load would increase and thus the LFTs would become more accurate), whereas if they were all taken on the same day, the viral load would be the same on each occasion and thus the probability of false negatives would be exactly the same for each of the 4 tests.
However, I was quite loudly told that my calculations were completely wrong, because the false negatives were not independent of one another [this is the bit I don't get, mathematically] and because if it was the case that each was equally likely to give a false negative, we would be being asked to do many tests at a time to reduce false negatives [I suspect even if sensible, we are not being told to do this because it makes the false negative issue so much more visible).
Have I gone wrong, and if so, where?