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

Question

The chartered financial analyst (CFA) is a designation earned after taking 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 0.53, 0.79, and 0.86, 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. 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?

Explanation / Answer

No of candidates that will be passed = 3000*0.53+2500*0.79+2000*0.86 = 5285

No of candidates took the exam = 3000+2500+2000 = 7500

P(Passed) = 5285/7500 = 0.7047

P(CFA 1/Passed) = ((3000*0.53)/7500)/0.7047 = 0.30084

So, answer is 0.30084

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