The prerequisite for Chem-201 at a college is Chem-101 or instructor approval. Suppose 90% of the students in Chem-201 had taken Chem-101, and of them, 69% passed Chem-201. Furthermore, of the students who passed Chem-201, 89.1% had taken Chem-101 beforehand. A student in Chem-201 is randomly chosen. a) Find the probability that the student passed Chem-201. b) Find the probability that the student enrolled in Chem-201 with instructor approval, given that the student failed the course. a) The probability that the student passed Chem-201 is 0.6970 (Do not round until the final answer. Then round to four decimal places as needed.) b) The probability that the student enrolled in Chem-201 with instructor approval, given that the student failed the course is (Do not round until the final answer. Then round to four decimal places as needed.)

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