Bender Electronics buys keyboards for its computers from another company. The ke

Question

Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 100 boxes, each box containing 20 keyboards. The quality control department at Bender Electronics first randomly selects one box from each shipment and then randomly selects 5 key boards from that box. The shipment is accepted if not more than 1 of the 5 keyboards is defective. The quality control inspector at Bender Electronics selected a box from a recently received shipment of keyboards. Unknown to the inspector, this box contains 6 defective keyboards. What is the probability that this shipment will be accepted? What is the probability that this shipment will not be accepted?

Explanation / Answer

P(defective) = 6 / 20 = 0.3

a) P(accepting the shipment) = P(0 defectiveout of 5) + P(1 defective out of 5)

                                               = 5C0 * 0.30 * 0.75 + 5C1 * 0.31 * 0.74

                                               = 0.5282

b) P(not accepting the shipment) = 1 - P(accepting the shipment)

                                                     = 1 - 0.5282

                                                     = 0.4718

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