Question: Refer to Exercise 6.74. 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 CFA I exam?

(Exercise 6.74)

The chartered financial analyst (CFA) is a designation earned after a candidate has taken three annual exams (CFA I, II, and 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 .57, .73, and .85, respectively. Suppose that 3,000 candidates take the level I exam, 2,500 take the level II exam, and 2,000 take the level III exam. Suppose that one student is selected at random. What is the probability that he or she has passed the exam?

Answer (that I got/did):

P(l) = test l ; P(ll) = test 2 ; P(lll) = test 3

P(l)= .57x3k= 1710

P(ll)= .73x2.5k= 1825

P(lll)= .85x2k= 1700

P(all candidates total)= 3k+2.5k+2k= 7500

P(all candidates who passed exams)= P(l)+P(ll)+P(lll)= 1710+1825+1700= 5235

P(pass all exams)= P(all candidates who passed exams)/P(all candidates total)= 5235/7500= 0.698