An additional qualification (A.Q) course was offered at three York faculties. Among 500 students, 160 students took the A.Q. course at the faculty of education (E), 290 students at the faculty of science (s), and the rest of the students at the faculty of health (H). The students from the faculty of education(E), and the faculty of Science (S), who failed (F) the A.Q. course, was 39%, and % respectively. The percentage of Students from the Faculty of Health (H) and who failed (F) the A.Q. course, was 2.5%.

a) One student is selected randomly among those who took the A.Q. course. What is the probability that the selected student failed the A.Q. course?

b) If the selected student passed (P) the A.Q. course, what is the probability that the student took the A.Q. course at the Faculty of Science (S)?

c) Are " Faculty of Education" and "failed" independent events? Your answer must include supporting probability calculations.

d) What is the probability that the student took the A.Q. course at the Faculty of Education or failed the A.Q. course? Let's assume the events Faculty of Education and failed didn't occur at the same time.