Two Basic Rules of Probability · Exercise 31

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 $\cap$ E).
(b) Find P(E$|$D).
(c) Find P(D $\cup$ 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, Introductory Business Statistics 2e · §3.3 Two Basic Rules of Probability · Exercise 31