A professor gives students a pop quiz with 5 true or false questions. Eighty percent of the students are well-prepared for the pop quiz, but twenty percent are not. Students who are prepared have a 85% chance of answering each question correctly, but the students who are unprepared simply randomly guess and have a 50% chance. Find the probability that a student was well-prepared under the following scenarios: (a) Answered 1 correctly (b) Answered 2 correctly (c) Answered 3 correctly (d) Answered 4 correctly