Question

A professor finds that she awards a final grade of A to 20% of the students. Of those who obtained a final grade of A, 70% obtained an A in the midterm examination. Also, 10% of students who did not obtain a final grade of A earned an A in the midterm exam. a. What is the percentage of the students who earned an A in the midterm examination? b. What is the probability that a student with an A on the midterm examination will obtain a final grade of A? c. What is the probability that a student with an A on the midterm examination will not obtain a final grade of A? d. Are the events "obtained an A in the midterm exam" and "obtained a final grade of A" collectively exhaustive? Justify your answer statistically.

Answer 1

Solution: Let us assume, total number of students 100 Number of students who were awarded final grade of A 100 x 20% = 20 Of the above 20 students, number of students who were awarded midterm grade of A = 20 x 70% 14 Number of students who were not awarded final grade of A 100 20 80 Of the above 80 students, number of students who were awarded midterm grade of A 80 x 10 % 8 Part-A: Percentage of students who earned an A in the midterm examination: 14 8 x 100 100 22% Part-B: Probability that a student with an A on the midterm examination will obtain a final grade of A 14 14 8 0.6364 Part-C: Probability that a student with an A on the midterm examination will not obtain a final grade of A 8 14 8 0.3636

Part-D: Let event A "Obtained an A in the midterm examination" Event B "Obtained a final grade of A" P(A U B) P(A) P(B) P(An B) P(A U B) 0.22 0.20 0.14 P(A U B) 0.28 Since P(A U B) 1, the events are not collectively exhaustive