The chartered financial analyst (CFA) is a designation earned after taking three annual exams

(level I, level II and level III). The exams are taken in early June. Candidates who pass an exam are

eligible to take the exam for the next level in the following year. The pass rates for levels I, II and

III are 0.57, 0.73 and 0.85 respectively. Suppose that 3,000 candidates take the level I exam, 2500

take the level II exam and 2000 take the level III exam.

(a) Suppose that one student is selected at random. What is the probability that he or she has

passed the exam?

(b) A randomly selected candidate who took a CFA exam tells you that he has passed the exam.

What is the probability that he took the level I exam?