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 0.51, 0.76, 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

The probability will be "0.2971".

According to the question,

The passing rate for the levels 1, 2 and 3 are:

Now,

The no. of students who passes CFA 1 will be:

=

=

The no. of students who passes CFA 2 will be:

=

=

The no. of students who passes CFA 3 will be:

=

=

So,

The total number of students who passes,

=

=

hence,

The probability that randomly selected candidates who took the CFA 1 will be:

=

=

=

Thus the above approach is correct.

Learn more:

link

The probability that he took the CFA I exam is 0.297.

Step-by-step explanation:

We are given that the pass rates for levels I, II, and III are 0.51, 0.76, 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.

Let the probability that the candidate take the level I exam = P(A) = =

The probability that the candidate take the level II exam = P(B) = =

The probability that the candidate take the level II exam = P(C) = =

Let P = event that the candidate is passed

Also, the probability of the pass rate for level I = P(P/A) = 0.51

The probability of the pass rate for level II = P(P/B) = 0.76

The probability of the pass rate for level III = P(P/C) = 0.86

Now, a randomly selected candidate who took a CFA exam tells you that he has passed the exam, the probability that he took the CFA I exam is given by = P(A/P)

We calculate this probability using the Bayes' Theorem;

       P(A/P) =

                  =

                  = = 0.297

Hence, the probability that he took the CFA I exam is 0.297.

you have 6 cupcakes