Counterpoint here, the false positive paradox won't surprise many physicians. It stems from concepts that are well-known among my colleagues and have been tested on each of my licensure exams. We apply them at least 10s of times each day.
I will add my anecdote to support this comment. Being an EE with probability-heavy background, I tried to give a
"you guys don't use prior probabilities" sermon to a physician and his physician-in-training daughter. I was made to eat my words by their reply, which was essentially that it is something they are all taught and use all the time in assessing risks, interpreting results, etc.
The one time I had to pay $500 for some tests not covered by insurance, but egregiously wrong in the context of my ailment, the referral was from a nurse practitioner.
Two things:
1. Perhaps doctors don't uniformly apply their training in interpreting test results and analyzing risks? (It is after all, quite common in all professions to forget some parts of one's training)
2. In addition to doctors, there are also technicians and nurse practitioners, who some times may not have the rigorous training that one associates with med school.
You can read more about those concepts here- (Note: "a priori" === "pretest probability" in MD speak) http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2636062/ https://en.wikipedia.org/wiki/Likelihood_ratios_in_diagnosti...