A hardware store has received two shipments of halogen lamps. The rst shipment contains 100 lamps, 4% of which are defective. The second shipment contains 50 lamps, 6% of which are defective. Suppose that Emanuel picks a lamp (at random) o of the shelf and purchases it, and he later discovers that the lamp he purchased is defective. Is the defective lamp more likely to come from the rst shipment or from the second shipment? Explain your reasoning clearly. Show the necessary steps that lead to your conclusion.