please help with both questions and all parts for them. thank you!

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) Find P(D AND E). - Part (b) Find P(E | D). Part (6) Find P(D OR E). El Part (d) Are D and E independent? Explain. O D and E are dependent events because pm I E) P(D)- O D and E are independent events because P(D | E) = P(D). O D and E are dependent events because P(D AND E) = 0.5. O D and E are independent events because they are mutually exclusive. Are D and E mutually exclusive? Explain. O The events are mutually exclusive because they are independent. 0 The events are not mutually exclusive because P(D AND E) 0. O The events are not mutually exclusive, which means they can be added together, and the sum is not 0.2. O The events are mutually exclusive because PgD AND E) = 0. The following table identifies a group of children by one of four hair colors, and by type of hair. Hair Type Brown Blond Black Red Totals Wavy 21 15 5 47 Straight 79 14 12 Totals 20 218 - Part (a) Complete the table. Hair Type Brown Blond Black Red Totals Wavy 21 15 Straight 79 14 C] 12 C] Totals C] 20 C] C] 218 Part (b) What is the probability that a randomly selected child will have wavy hair? (Enter your answer as a fraction.) U - Part (c) What is the probability that a randomly selected child will have either brown or blond hair? (Enter your answer as a fraction.) U Part (I!) What is the probability that a randomly selected child will have wavy brown hair? (Enter your answer as a fraction.) U 3 Part (e) What is the probability that a randomly selected child will have red hair, given that he has straight hair'? (Enter your answer as a fraction.) 3 Part (f) If B is the event of a child having brown hair, nd the probability of the complement of B. (Enter your answer as a fraction.) 3 Part (9) If B is the event of a child having brown hair, what does the complement of B represent? 0 The complement of B would be the event of a child having wavy or straight hair. 0 The complement of B would be the event of a child having blond or black hair. 0 The complement of B would be the event of a child having blond hair. 0 The complement of B would be the event of a child not having brown hair