6.13 A graduate wants to pursue a career in a profession. She will need to gain membership of the professional institute by passing three stages of examinations. If she becomes a full member of the institute she anticipates that she will be able to earn £50 000 per year. If she fails the final stage of the examinations, but passes the first two stages she can become an associate member of the institute. An associate member earns about £32 000 per year. If she fails at the second stage but passes the initial stage she can obtain a certificate of competence from the institute and probably earn £24 000. If she fails the initial stage of the examinations she will have to consider other employment and anticipates that she would be able to earn £18 000. The pass rates for the initial, second and final stages of the institute’s examinations are 70 per cent, 55 per cent, and 80 per cent.

What is the expected value of her annual earnings?