6.87 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 remedy 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% are produced by A2 and 20% are produced by A3.

a. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R)

and another for no rework (N). Then enter appropriate probabilities on the branches.

b. What is the probability that a randomly selected component came from A1 and needed rework?

c. What is the probability that a randomly selected component needed rework?