A company uses three different assembly lines—A1,A2, and A3—to manufacture a particular component. Of those manufactured by line A1, 5% need rework to remedy a defect, whereas 8% of A2’s components need rework and 10% of A3’s need rework. Suppose that 50% of all components are produced by line A1, 30% are produced by line A2, and 20% come from line A3. If a randomly selected component needs rework, what is the probability that it came from line A1? From line A2? From line A3?
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