Please help with all parts. Thank you!

A college finds that 8% of students have taken a distance learning class and that 20% 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. Find P(D AND E). Find P(E| D). Find P(D OR E). Are D and E independent? Explain. O D and E are independent events because P(D| E) = P(D). O D and E are independent events because they are mutually exclusive. 0 D and E are dependent events because P(D AND E) = 0.5. O D and E are dependent events because P(D | E) P(D)- 3 Part (e) Are D and E mutually exclusive? Explain. O The events are mutually exclusive because they are independent. 0 The events are not mutually exclusive, which means they can be added together, and the sum is not 0.2. O The events are not mutually exclusive because P(D AND E) 0_ O The events are mutually exclusive because P(D AND E) = 0