document.write( "Question 1181356: 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?\r
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Algebra.Com's Answer #811257 by ikleyn(52794)\"\" \"About 
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\n" ); document.write( "Ace Machine Works estimates that the probability its lather tool is properly adjusted is 0.8.
\n" ); document.write( "When the lathe is properly adjusted, there is a 0.9 probability that parts produced pass inspection.
\n" ); document.write( "If the lathe is out of adjustment, however, the probability of a good part being produced is only 0.2.
\n" ); document.write( "A part randomly chosen is inspected and found it to be acceptable. At this point,
\n" ); document.write( "what is the posterior probability that the lathe tool is properly adjusted?
\n" ); document.write( "Please provide steps to solve this problem. Thank you
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\n" ); document.write( "\n" ); document.write( "            In this problem, they want you find the  CONDITIONAL  probability, \r
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\n" ); document.write( "\n" ); document.write( "            They want you guess it   - - -   the correct guessing \r
\n" ); document.write( "\n" ); document.write( "            is a  PART  of the problem's solution  (and is its  MAJOR  part).\r
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document.write( "So they want you find the conditional probability  \r\n" );
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document.write( "        P(lathe tool is properly adjusted given the randomly chosen part is acceptable).\r\n" );
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document.write( "In more formal way, they want you find \r\n" );
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document.write( "       P(lathe tool is properly adjusted | the randomly chosen part is acceptable) = \r\n" );
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document.write( "    = P(lathe tool is properly adjusted AND the randomly chosen part is acceptable) / P(the randomly chosen part is acceptable).\r\n" );
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document.write( "Regarding the numerator of this fraction, it is equal to\r\n" );
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document.write( "     P(lathe tool is properly adjusted AND the randomly chosen part is acceptable) = 0.8*0.9 = 0.72.\r\n" );
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document.write( "Regarding the denominator, it is equal to\r\n" );
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document.write( "    P(the randomly chosen part is acceptable) = 0.8*0.9 + (1-0.8)*0.2 = 0.76.\r\n" );
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document.write( "THEREFORE, combining these circumstances, we find the answer\r\n" );
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document.write( "    P(lathe tool is properly adjusted given the randomly chosen part is acceptable) = \"0.72%2F0.76\" = use your calculator = 0.9474 (rounded).\r\n" );
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document.write( "ANSWER.  The posterior probability that the lathe tool is properly adjusted  is equal to  0.9474,  or  94.74%.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and carefully explained.\r
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\n" ); document.write( "\n" ); document.write( "And you have now the mantra in your archive to pronounce it every time as you solve similar problem.\r
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\n" ); document.write( "\n" ); document.write( "On conditional probability,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Conditional probability problems \r
\n" ); document.write( "\n" ); document.write( "    - Conditional probability problems REVISITED \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Read them to develop your skills and knowledge.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Solved problems on Probability\"
\n" ); document.write( "and  \"Additional problems on Probability\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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