Respuesta :
Answer:
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) = [tex]\frac{3000}{7500}[/tex] = [tex]\frac{2}{5}[/tex]
The probability that the candidate take the level II exam = P(B) = [tex]\frac{2500}{7500}[/tex] = [tex]\frac{1}{3}[/tex]
The probability that the candidate take the level II exam = P(C) = [tex]\frac{2000}{7500}[/tex] = [tex]\frac{4}{15}[/tex]
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) = [tex]\frac{P(A) \times P(P/A)}{P(A) \times P(P/A)+P(B) \times P(P/B)+P(C) \times P(P/C)}[/tex]
= [tex]\frac{\frac{2}{5}\times 0.51 }{\frac{2}{5}\times 0.51+\frac{1}{3}\times 0.76+\frac{4}{15}\times 0.86}[/tex]
= [tex]\frac{0.204}{0.687}[/tex] = 0.297
Hence, the probability that he took the CFA I exam is 0.297.
The probability will be "0.2971".
According to the question,
The passing rate for the levels 1, 2 and 3 are:
- 0.51
- 0.76
- 0.86
Now,
The no. of students who passes CFA 1 will be:
= [tex]3000\times 0.51[/tex]
= [tex]1530[/tex]
The no. of students who passes CFA 2 will be:
= [tex]2500\times 0.76[/tex]
= [tex]1900[/tex]
The no. of students who passes CFA 3 will be:
= [tex]2000\times 0.86[/tex]
= [tex]1720[/tex]
So,
The total number of students who passes,
= [tex]1530+1900+1720[/tex]
= [tex]5150[/tex]
hence,
The probability that randomly selected candidates who took the CFA 1 will be:
= [tex]\frac{Favorable \ events}{Total \ events}[/tex]
= [tex]\frac{1530}{5150}[/tex]
= [tex]0.2971[/tex]
Thus the above approach is correct.
Learn more:
https://brainly.com/question/14869014
