Lesson Probabilistic analysis of testing procedures in industry
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<H2>Probabilistic analysis of testing procedures in industry</H2> <H3>Problem 1</H3>Ace Machine Works estimates that the probability its lather tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that parts produced pass inspection. If the lathe is out of adjustment, however, the probability of a good part being produced is only 0.2. A part randomly chosen is inspected and found it to be acceptable. At this point, what is the posterior probability that the lathe tool is properly adjusted? <B>Solution</B> In this problem, they want you find the CONDITIONAL probability, although they do not pronounce this term. They want you guess it - - - the correct guessing is a PART of the problem's solution (and is its MAJOR part). <pre> So they want you find the conditional probability P(lathe tool is properly adjusted given the randomly chosen part is acceptable). In more formal way, they want you find P(lathe tool is properly adjusted | the randomly chosen part is acceptable) = = P(lathe tool is properly adjusted AND the randomly chosen part is acceptable) / P(the randomly chosen part is acceptable). Regarding the numerator of this fraction, it is equal to P(lathe tool is properly adjusted AND the randomly chosen part is acceptable) = 0.8*0.9 = 0.72. Regarding the denominator, it is equal to P(the randomly chosen part is acceptable) = 0.8*0.9 + (1-0.8)*0.2 = 0.76. THEREFORE, combining these circumstances, we find the answer P(lathe tool is properly adjusted given the randomly chosen part is acceptable) = {{{0.72/0.76}}} = use your calculator = 0.9474 (rounded). <U>ANSWER</U>. 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