Say that the symptoms of a very rare disease show up in a million people, most of whom do not actually have that disease. But because of those symptoms, doctors order a test. It is known that about 5% of those with symptoms are actually infected. Thus, if the test was perfect there would be about 50,000 positive results. But the test isn’t perfect. Say it gives 8% false positives and 10% false negatives. So, 5000 of the 50,000 who should test positive test negative instead. 76,000 of the 950,000 who should test negative, test positive instead. Altogether there will be 121,000 positive tests of which only 45,000 are correct. There is a 62.8% chance you are uninfected when you get a positive test result in this hypothetical (but not uncommon) scenario. Note that you wouldn’t be far off if you simply compared the false positive rate with the rate of infection among those tested. 8 vs five is 61.5%.