Question: (9) In a calculus course, the instructor gave an algebra exam on the rst day of class to help students determine whether or not they

(9) In a calculus course, the instructor gave an algebra exam on the rst day of class to help students determine whether or not they had enrolled in the appropriate course. 80% of the students in the class passed the exam. 40% of those who passed the exam on the rst day of class earned an A in the course, whereas only 20% of those who failed the exam earned an A in the course. What is the probability that a student selected at random passed the exam on the rst day of class, given that they earned an A in the course? (10) A factory has two machines that produce bolts. Machine I produces 60% of the daily output of bolts, and 3% of its bolts are defective. Machine 11 produces 40% of the daily output, and 2% of its bolts are defective. (a) What is the probability that a bolt selected at random will be defective? (b) If a bolt is selected at random and found to be defective, what is the probability that it was produced by machine

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