About 2%: Manrai and colleagues get 1.96% for a test that misses no case. The disease is so rare that the people who test positive without having it far outnumber the people who have it. In 2013 they asked 61 physicians, residents and medical students at a Boston-area hospital a looser wording of this question, which gave a “false positive rate of 5%” and did not say whether the test missed any case: 14 answered correctly, and the most common answer, given by 27 of them, was 95% (Manrai et al., 2014).
Manrai, A. K., Bhatia, G., Strymish, J., Kohane, I. S., & Jain, S. H. (2014). Medicine’s Uncomfortable Relationship With Math. JAMA Internal Medicine, 174(6), 991.