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A hardware store has received two shipments of halogen lamps. The first 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) off of the shelf and purchases it, and he later discovers that the lamp he purchased is defective. What is the probability that the defect came with the first shipment?

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