Question

Printed circuit cards are placed in a functional test after being populated with semiconductor chips. a lot contains 140 cards, and 20 are selected without replacement for func- tional testing. (a) if 20 cards are defective, what is the probability that at least 1 defective card is in the sample? (b) if 5 cards are defective, what is the probability that at least 1 defective card appears in the sample? (montgomery 97) montgomery, douglas

c. applied statistics and probability for engineers, 6th edition. wiley, 2013-10-21. vitalbook file. the citation provided is a guideline. please check each citation for accuracy before use.

Answer 1

a) If 20 cards are defective, 120 are not. There are C(120, 20) ≈ 2.946·10²² ways to choose 20 cards of which none are defective. There are C(140, 20) ≈ 8.272·10²³ ways to choose 20 cards. So, the probability of choosing 20 cards of which none are defective is about 2.946/82.72 ≈ 0.03562. This means the probability that at least one is defective is
1 - 0.03562 ≈ 0.96438

b) Similarly, 1 - C(135, 20)/C(140, 20) ≈ 0.54294


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C(n, k) = n!/(k!(n-k)!)