A factory received a shipment of 28 compressors, and the vendor who sold the items knows there are 7 compressors in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the compressors in the sample are defective, he will refuse the shipment. If a sample of 7 compressors is selected, find the probability that none in the sample are defective.
Answers
Given : a shipment of 28 compressors , 7 compressors in the shipment are defective.
a sample of 7 compressors is selected,
To Find : probability that none in the sample are defective.
Solution:
Total compressors = 28
Defective compressors = 7
Non Defective compressors = 28 - 7 = 21
a sample of 7 compressors is selected
Ways to select 7 compressors out of 28 = ²⁸C₇
Ways to select 7 compressors such that none is defectives = ²¹C₇.⁷C₀
= ²¹C₇
probability that none in the sample are defective. = ²¹C₇/ ²⁸C₇
21 * 20 * 19 * 18 * 17 * 16 * 15 /(28 * 27 * 26 * 25 * 24 * 23 * 22)
= 0.09821
probability that none in the sample are defective is about 0.09821
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