An inspector selects a sample of 12 items at random from acollection of 60 items

Question

An inspector selects a sample of 12 items at random from acollection of 60 items, of which 18 have excellent quality, 25 havegood quality, 12 have poor, and 5 are defective. 1) what is the probability that the sample only contains itemsthat have either excellent or good quality? 2) what is the probability that the sample contains 3 ofexcellent, 3 of good, 3 of poor, and 3 defective? An inspector selects a sample of 12 items at random from acollection of 60 items, of which 18 have excellent quality, 25 havegood quality, 12 have poor, and 5 are defective. 1) what is the probability that the sample only contains itemsthat have either excellent or good quality? 2) what is the probability that the sample contains 3 ofexcellent, 3 of good, 3 of poor, and 3 defective?

Explanation / Answer

Let C(n,r ) be the number ofcombinations of n things chosen r at a time. Part 1: Part 1: P(either excellent orgood)=C(18,x)C(25,12-x)/C(60,12) Summation is from x=0 to x=12 inthe above equation. Part 2:

P(3E,3G,3P,3D)=C(18,3)C(25,3)C(12,3)C(5,3)/C(60,12)

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