Use the tree made from question 1 (rewritten below) to answer the question.
A company uses three different assembly lines - A1, A2, and A3- to manufacture a particular component. Of those manufactured by A1, 5% need rework to fix a defect, whereas 8% of A2's components, and 10% of A3's components need rework. Suppose that 50% of all components are produced by A1, 30% by A2, and 20% by A3.
What is the probability that a randomly selected component needed rework?