In biology class, 40% of the students are light studiers, 60% are moderate or heavy studiers. Given that a student is a light studier, the probability of failing the course is 0.2, given that a student is a moderate or heavy studier, the probability of failing the course is 0.05

(a) What is the probability that a randomly selected student from this course will fail?

(b) If a student failed the course, what is the probability that he or she is a light studier?