A college finds that 10% of students have taken a distance learning class and that 40% of students are part time students. Of the part time students, 20% have taken a distance learning class. Let D = event that a student takes a distance learning class and E = event that a student is a part time student a. Find P(D AND E). b. Find P(E|D). c. Find P(D OR E). d. Using an appropriate test, show whether D and E are independent. e. Using an appropriate test, show whether D and E are mutually exclusive.