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 0.55, 0.72, and 0.89, 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 of the 7,500 candidates is selected at random. What is the probability that he or she passes the exam?
The probability of candidate pass level I exam is out of 7500 is = (3000C1) / (7500C1) = 0.4
The probability of candidate pass level II exam is out of 7500 is = (2500C1) / (7500C1) = 0.333
The probability of candidate pass level III exam is out of 7500 is = (2000C1) / (7500C1) = 0.267
Therefore the probability that candidate pass all 3 level of exam= probability of candidate pass level III exam = 0.267
Because, Candidates who pass an exam are eligible to take the exam for the next level.
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