HDC produces microcomputer hard drives at four different production facilities (
ID: 3042369 • Letter: H
Question
HDC produces microcomputer hard drives at four different production facilities (F1, F2, F3, and F4) Hard drive production at F1, F2, F3, and F4 is 20%, 25%, 15%, and 40%, respectively. Quality control records indicate that 1.5%, 2%, 1%, and 3% of the hard drives are defective at F1, F2, F3, and F4, respectively.
a. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F2?
b. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F4?
c. If an HDC hard drive is picked at random, what is the probability that it is non-defective?
Explanation / Answer
probability of defecitve =P(F1 and defective+F2 and defective+F3 and defective+F4 and defective)
=0.2*0.015+0.25*0.02+0.15*0.01+0.4*0.03=0.0215
a) probability that it was produced at F2 given defective
=P(F2 and defective)/P(defective) =0.25*0.02/0.0215 =0.2326
b)
probability that it was produced at F4 given defective
=P(F4 and defective)/P(defective) =0.4*0.03/0.0215 =0.5581
c)
probability that it is non-defective =1-P(defective) =1-0.0215 =0.9785
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