I'm confused on this part of my homework. Any help would be great

Question

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.

Part a)

1. Find P(D AND E).

Part b)

1. Find P(E | D).

Part c)

1. Find P(D OR E).

Are D and E independent?

Are D and E mutually exclusive?

Answer 1

A) P (D and E) = 0.4 x 0.2 = 0.08

explanation: 20% of the part times students are taking distance learning classes (D and E)

B) P (E | D) = P ( D and E) / P (D) = 0.08 / 0.1 = 0.8

C) P (D or E) = 0.4 + 0.1 - 0.08 = 0.42

D and E are not independent, because P (D and E) doesn't equal P(D) x P(E)

D and E are not mutually exclusive