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 0 = event that a student takes a distance learning class and E = event that a student is a part time student.

a. Find 90 AND E).

b. Find P(aD).

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.