A company uses three different assembly lines – A1, A2, and A3 – to manufacture a...

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.
1. (a) Suppose a component is selected at random, what is the probability that it needs rework?
2. (b) If a randomly selected component needs rework, what is the probability that it came from line A1?
3. (c) If a randomly selected component (((((((does not))))))) need rework, what is the proba- bility that it came from line A2?

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