3 ms·
About 0.01%, or 1 in 10,000. Consider a population of 100M people, of which 100 would have the illness. Of them, 99% = 99 would test positive and 1% = 1 would
by akrolsmir 11y ago
About 0.01%, or 1 in 10,000.
Consider a population of 100M people, of which 100 would have the illness. Of them, 99% = 99 would test positive and 1% = 1 would test negative. For the other 99,999,900 healthy people, 99% = 98,999,901 would test negative and 1% = 999,999 would test positive.
In total, 99 + 999,999 people would test positive. Given that a person tests positive, then, there is only a 99 / (99 + 999,999) ~= 0.01% chance that person has the illness.
- pif 11y agoYour answer is as problematic as dsp1234's one.
- akrolsmir 11y agoFor sure, this assumes that false positive rate = false negative rate = 1%, but it suffices to illustrate how a highly accurate test can produce misleading results. A solution would be repeated retesting, as the 1st, 2nd, 3rd, and 4th consecutive positive test results would lead to 0.01%, 1%, 50%, and 99% chances. (Each additional positive test reduces the false positives by 100-fold, whereas the ill patients are very likely to get continually positive results.)
- adrianN 11y agoOnly if your tests are all independent. Doing the same test twice probably doesn't buy you anything.