Two Basic Rules of Probability · Exercise 31

A college finds that 10 percent of students have taken a distance learning class and that 40 percent of students are part-time students. Of the part-time students, 20 percent 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.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §3.3 Two Basic Rules of Probability · Exercise 31