Suppose that 60% of the students do homework regularly.
It is also known that 80% of students, who had been doing homework regularly, end up doing well in the course (get a grade of A or B). Only 20% of students, who had not been doing homework regularly, end up doing well in the course.
a. What is the probability that a student does well in the course?
b. Given that the student did well in the course, what is the probability that the student had been doing homework regularly?