Science PhD's are on roughly the same ground as those poor MDs who didn't know what a positive test result does not imply high chances of having a rare disease.

Science PhD's are on roughly the same ground as those poor MDs who didn't know what a positive test result does not imply high chances of having a rare disease. Statistics can be non-intuitive because common sense only ever approximates it at best. You've got to either always run the math or build some good heuristics for when to expect that common sense just failed you.