document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111403>Question 1111403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It is known that of the articles produced by a factory, 20% come from Machine A, 30% from Machine B, and 50% from Machine C. The percentages of satisfactory articles among those produced are 95% for A, 85% for B and 90% for C. An article is chosen at random.<BR>\n" );
document.write( "What is the probability that is satisfactory?<BR>\n" );
document.write( "Assuming that the article is not satisfactory, what is the probability that it was produced by B?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726412 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let T equal the total numbert of articles produced.\r<BR>\n" );
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document.write( "the articles that come from A = .2T<BR>\n" );
document.write( "the articles that come from B = .3T<BR>\n" );
document.write( "the articles that come from C = .5T\r<BR>\n" );
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document.write( "you get .2T + .3T + .5T = T\r<BR>\n" );
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document.write( "95% of the articles produced by A are satisfactory.<BR>\n" );
document.write( "85% of the articles produced by B are satisfactory.<BR>\n" );
document.write( "90% of the articles produced by Care satisfactory.\r<BR>\n" );
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document.write( ".95A + .85B + .9C = S, where S equals the total satisfactory articles produced.\r<BR>\n" );
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document.write( "since A = .2T and B = .3T and C = .5T, then:\r<BR>\n" );
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document.write( ".95 * .2T + .85 * .3T + .9 * .5T = S<BR>\n" );
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document.write( "this gets you S = .895T.\r<BR>\n" );
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document.write( "this means 89.5% of all the articles produced are satisfactory.\r<BR>\n" );
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document.write( "if you let N equal the total number of articles that are not satisfactory, then:\r<BR>\n" );
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document.write( "S + N = T\r<BR>\n" );
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document.write( "solve for N to get N = T - S\r<BR>\n" );
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document.write( "since S = .895T, you get N = T - .895T which results in N = .105T\r<BR>\n" );
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document.write( "this means that 10.5% of all the articles produced are not satisfactory.\r<BR>\n" );
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document.write( "since 85% of the articles produced by B are satisfactory, then 15% of the articles produced by B are not satisfactory.\r<BR>\n" );
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document.write( "since B = .3T, you get .15 * .3T = .045T.\r<BR>\n" );
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document.write( "this means that, out of all the articles that are produced, .45% of them are unsatisfactory articles that come from B.\r<BR>\n" );
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document.write( "since, out of all the articles that are produced, 10.5% of them are not satisfactory, then the ratio of the unsatisfactory articles that are produced by B to the total number of unsatisfactory articles is .045/.105, which is equal to .4285714286.\r<BR>\n" );
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document.write( "that means that 42.85714286% of the articles that are unsatisfactory come from B.\r<BR>\n" );
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document.write( "answers to your questions should be:\r<BR>\n" );
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document.write( "An article is chosen at random.\r<BR>\n" );
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document.write( "1. What is the probability that is satisfactory?\r<BR>\n" );
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document.write( "the probability that it is satisfactory is .895, or 89.5%.\r<BR>\n" );
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document.write( "2. Assuming that the article is not satisfactory, what is the probability that it was produced by B?\r<BR>\n" );
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document.write( "assuming that the articles is not satisfactory, the probability that it came from B is .4285714286, or 42.85714286%\r<BR>\n" );
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document.write( "if you round the ratio to 4 decimal places, then the percent will be rounded to 2 decimal places.\r<BR>\n" );
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document.write( "you will get the ratio is .4286 and the percent is 42.86%.\r<BR>\n" );
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document.write( "round your answers as required.\r<BR>\n" );
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document.write( "i believe this is what you are looking for.\r<BR>\n" );
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document.write( "let me know if it's not.<BR>\n" );
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