A company uses three different assembly lines—?A?1,?A?2, and ?A?3—to manufacture a particular component. Of those manufactured by line ?A?1, 5% need rework to remedy a defect, whereas 8% of ?A?2’s components need rework and 10% of ?A?3’s need rework. Suppose that 50% of all components are produced by line ?A?1, 30% are produced by line ?A?2, and 20% come from line ?A?3. If a randomly selected component needs rework, what is the probability that it came from line ?A?1? From line ?A?2? From lin? ?3?

Answer Step 1 of 5 P(A1)=0.5 P(A2)=0.3 P(A3)=0.2 Step 2 of 5 D is the event component needs rework P(D/A1)=0.05 P(D/A2)=0.08 P(D/A3)=0.1 Step 3 of 5 The probability that it came from line A1 P(DA1) = P(D|A1)P(A1) =0.05(0.5)=0.025