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 tests (CFA I,II, and III). The exams are taken in early June. Candidates who pass an test are eligible to take the test for the next level in the following year. The pass rates for levels I, II, and III are 0.57, 0.7, and 0.89, respectively. Suppose that 3,000 candidates take the level I test, 2,500 take the level II test and 2,000 take the level III test. A randomly selected candidate who took a CFA test tells you that he has passed the test. What is the probability that he took the CFA I test?

Explanation / Answer

solution=

n[passed CFA [ I ] ] = 3000*0.57 = 1710
n[passed CFA [ II ] ] = 2500*0.70 = 1750
n[passed CFA [ III ] ] = 2000*0.89 = 1780

n[ total passed ] = 5240

reqd. probability = favorable events / total events
= 1710 /5240
= 0.3263

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