document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206541>Question 1206541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A production process produces an item. On average 20% of all items produced are defective. Each item is inspected before being shipped. The inspector misclassifies an item 10% of the time, i.e. probability (classified/defective item) = Probability (classified defective/good item).<BR>\n" );
document.write( "a. What proportions of the items will be classified defective.<BR>\n" );
document.write( "b. Suppose that only items classified as good after inspection are shipped;<BR>\n" );
document.write( "(i). What percentage of the items shipped are good.<BR>\n" );
document.write( "(ii). What percentage of those shipped are good. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844089 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=844089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to be reviewed and re-posted when more time is available.<BR>\n" );
document.write( "stay tuned.\r<BR>\n" );
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document.write( "80% of the total are actually good.<BR>\n" );
document.write( "20% of the total are actually defective.\r<BR>\n" );
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document.write( "10% of the good are mis-classified as defective.<BR>\n" );
document.write( "10% * 80% = 8% that are mis-classified as defective.<BR>\n" );
document.write( "that leaves 80% minus 8% = 72% that are correctly classified as good.\r<BR>\n" );
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document.write( "10% of the defective are mis-classified as good.<BR>\n" );
document.write( "10% * 20% = 2% that are mis-classified as good.<BR>\n" );
document.write( "that leaves 20% minus 2% = 18% that are correctly classified as defective.\r<BR>\n" );
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document.write( "you have 72% that are correctly classified as good and 2% that are incorrectly classified as good for a total of 74% classified as good.\r<BR>\n" );
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document.write( "you have 18% that are correctly classified as defective and 8% that are incorrectly classified as defective for a total of 26% classified as defective.\r<BR>\n" );
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document.write( "totals look good.\r<BR>\n" );
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document.write( "80% actually good plus 20% actually defective = 100% total.<BR>\n" );
document.write( "74% classified good plus 26% classified defective = 100% total.\r<BR>\n" );
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document.write( "this agrees with my original assessment.<BR>\n" );
document.write( "let me know if you have any questions or concerns.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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