>>116646981% actually infected. Test arent consequential to actual infection. Even as a semantic argument this is questionable. the question is asking about your own chance of being infected given two facts. testing positive using a 99% accurate test doesn't mean you necessarily have a 99% chance of being positive. i tried to show it by assuming this is true and then seeing what happens when you get tested twice and get two results. it leads to you having a 99% chance of being positive and a 99% chance of being negative. either you accept this, and find some way of explaining what this means, or you have to give up on something.
Conceptually, it is a tricky question, but ok. The answer is 0.1%, because the detection of the virus does not change the state of health of the individual. You either have or do not have an infection of corona virus. Then, you either know it or you don't. Also, accuracy it's not the right term in this regard.
COVID-19 affects 0.1% of the population, n.
Unaffected = 0.999n
Affected = 0.001n
If n are tested
Indepenent Probability of false positive = Unaffected * Chance of inaccuracy = 0.999n * 0.01 = 0.00999n
Independent Probability of true positive = Affected * Chance of accuracy = 0.001n * 0.99 = 0.00099n
Probability of true positive = 0.00099n/(0.00099n + 0.00999n) ~= 9%.
clearly that's not the right approach if the question comes with multiple choices and your answer is indeterminate.
of course you could just attack the premise of the question but that doesn't help anybody
1000 x 0.1% = one infected
1000 x 1% false pos = 10 false pos
1/11 = 9% Cool
Now what happens when it’s like real life and we have Switzerland at 9.7%, Sweden at 10, Madrid at 11%, NYC at 20, etc
100000 people tested
0.1% are sick = 100 people
99.9% are healthy = 99900 people
test accuracy 99%
of the 100 sick, 99 will test as positive
of the 100 sick, 1 will test as negative (FN)
of the 99900 healthy, 999 will test as positive (FP)
