Settle down you numerophobes. Daylight Atheism has a very fascinating exercise in critical thinking, and it’s worth reading whether you’re a mathematician or not. If you have a positive result from a blood test that’s 95% accurate, and it says you have a very rare disease, what are the odds you really have it? Surprisingly low!
A more intuitive way to explain this result is this: the test is highly accurate, but the disease is rare. Therefore, the vast majority of people who are tested won’t actually have it – and the number of false positives from that group, though small compared to the size of that group, is larger than the relatively small number of people who actually have the disease and correctly test positive.