Binomial Probability distribution

Question

A pharmaceutical company receives large shipments of ibuprofen tablets and uses this acceptance sampling plan: randomly select and test 30 tablets, then accept the whole batch if there is at most one that doesn't meet the required specifications. If a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects, what is the probability that this whole shipment will be accepted?

Answer 1

x = number of defect, probability (x = 0 or 1), when P(defect) = 0.15. n = 30 tablets

0 30

p(x = 0) = 30! 0.15 0.85 = 0.0076

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0! 30!

1 29

p(x = 1) = 30! 0.15 0.85 = 0.0404

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1! 29!

p(x = 0 or 1) = 0.0076 + 0.0404 = 0.048

probability shipment will be accepted = 1 - 0.048 = 0.952