Did you answer 95%? If you did, you're among the large majority of people,
not just among the general population but also practising clinicians,
who come to the same conclusion. And you'd be just as wrong as them. In
fact, the odds you have the disease are a little less than 2%. Here's how it
works. Let's assume an ensemble of 10,000 randomly selected people are tested.
On average, ten of these people will have the disease, and all of them will
test positive for it (no false negatives). But among that population, 500
people who do not have the disease will also test positive due to the 5% false
positive rate of the test. That means that, on average (it gets tedious repeating
this, but the natterers will be all over me if I don't do so in every instance),
there will be, of 10,000 people tested, a total of 510 positive results, of which
10 actually have the disease. Hence, if you're the recipient of a positive test
result, the probability you have the disease is 10/510, or a tad less than 2%.
So, before embarking upon a demanding and potentially dangerous treatment regime,
you're well advised to get some other independent tests to confirm that you
are actually afflicted.
In making important decisions in life, we often rely upon information from
past performance and reputation without taking into account how much those
results may be affected by randomness, luck, and the “survivor effect”
(the Russian roulette players who brag of their success in the game are
necessarily those who aren't yet dead). When choosing a dentist, you can
be pretty sure that a practitioner who is recommended by a variety of his
patients whom you respect will do an excellent job drilling your teeth. But
this is