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A factory received a shipment of 13 bolts, and the vendor who sold the items knows there are 8 bolts in the shipment that are defective and 5 are not defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the bolts in the sample are defective, he will refuse the shipment. Give answer as a decimal to four decimal places.
(a) If a sample of 5 bolts is selected, find the probability that all in the sample are defective.
(b) If a sample of 5 bolts is selected, find the probability that 4 in the sample are defective.
(c) If a sample of 4 bolts is selected, find the probability that 1 in the sample are defective.
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