A certain financial professional designation is given to applicants who pass three examinations: levels I, II, and III. The pass rates for level I, II, and III are 57%, 73%, and 85%, respectively. 3000 applicants have just written the level I exam, 2500 have written level II, and 2000 have written level III.
a. What is the probability an applicant, randomly selected, has passed her/his exam?
b. If a randomly selected applicant is found to have passed, what is the probability s/he wrote the level I exam?