Answer:
The probability Mike Fishman completed the assignments is 0.8780.
Explanation:
Note: The question is not complete but the complete one is given as follows:
Dr. Barton has been teaching basic statistics for many years. He knows that 80 percent of the students will complete the assigned problems. He has also determined that among those who do complete the assignment, 90 percent will pass the course. Among these students who do not complete their assignments, 50 percent will pass. Mike Fishman took statistics last semester from Dr. Barton and received a passing grade. What is the probability he completed the assignments?
The following are now the explanation to the answer:
Let A denote the event that the assignment will be completed by the students, B denote the event that the assignment will not be completed by the students, and C denote the event that the test will be passed; the probability that Mike Fishman completed the assignments can be estimated using the following formula:
P(A|C) = P(A)P(C|A) / [P(A)P(C|A) + P(B)P(C|B)] .................. (1)
Where,
P(A|C) = The probability that Mike Fishman completed the assignments = ?
P(A) = Percentage of the students who will complete the assigned problems = 80%, or 0.80
P(B) = Percentage of the students who will not complete the assigned problems = 100% - 80% = 20%, or 0.20
P(C|A) = Percentage of students who do complete the assignment and pass the course = 90%, or 0.90
P(C|B) = Percentage of students who do not complete the assignment but pass the course = 50%, or 0.50
Substituting all the values into equation (1), we have:
P(A|C) = 0.80 * 0.90 / [(0.80 * 0.90) + (0.20 * 0.50)]
P(A|C) = 0.72 / (0.72 + 0.10)
P(A|C) = 0.72 / 0.82
P(A|C) = 0.8780
Therefore, the probability he completed the assignments is 0.8780.