Part II: Free response problems [50 points] Please answer the following free response questions. Show your work and justify your answers. You may either type your answers or write down your answers using a pen or an iPad. When you are finished, you should upload your answers to Gradescope. 11. [5 subproblems, 15 points] In a university, 45% of the students like music, 34% of the students like art, and 12% of the students like the both. A) What is the probability that a randomly chosen student likes neither music or art? B) What is the probability that a randomly chosen student likes music but not art? C) Randomly choose 4 students. What is the probability that exactly one of these 4 students likes music? D) If a student likes music, then he is 90% likely to enroll in a music course; otherwise, the probability that he enrolls in a music course is only 20%. What is the probability that a randomly chosen student enrolls in a music course? E) If we have known a student has enrolled in a music course, what is the probability that he likes music