Does performance improve when candidates resit a postgraduate examination?

Luck plays some role in passing any examination. When candidates pass a postgraduate examination at the second, third or subsequent attempt is it because their knowledge has truly improved or because they have at least been lucky? In this paper a simple model, requiring knowledge only of the pass rates at resits, and of the reliability of the examination, is applied to the MRCGP examination of the Royal College of General Practitioners. Candidates increase their true ability before second and third attempts at the examination, after which ability declines.