School band teacher. Of those who joined the marching band because they had been recommended, 90% are very good at what they do. Of those who joined the marching band and weren't recommended, only 60% are very good. A random High School marching band student is chosen. The student plays in front of experts who are qualified to judge a student as very good or not. For the purpose of this question, suppose the percentages in the sample match all percentages stated above. Find each probability and do not round answers unless told to: a) The High School student was recommended and was judged to be very good b) The student was very good, given that they were actually recommended C) The student was very good ) That if the student were good, they were recommended Round to 2 decimal positions.

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