document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265891>Question 265891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A production process produces an item. On average, 15% of all items produced are defective. Each item is inspected before being shipped, and the inspector misclassifies an item 10% of the time. What proportion of the items will be \"classified as good?\" What is the probability that an item is defective given that it was classified as good?\r<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 #195443 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=195443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A production process produces an item. On average, 15% of all items produced are defective. Each item is inspected before being shipped, and the inspector misclassifies an item 10% of the time. <BR>\n" );
document.write( "What proportion of the items will be \"classified as good?\" <BR>\n" );
document.write( "P(classed as good) = 90% of Good + 10% of Bad = 0.9*0.85+0.1(0.15)= 0.78<BR>\n" );
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document.write( "What is the probability that an item is defective given that it was classified as good? <BR>\n" );
document.write( "P(defect | classgood) = p(defect AND classgood)/P(classgood) <BR>\n" );
document.write( "= (0.1*0.15)/0.85 = 0.0176<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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