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
