document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81424>Question 81424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An electronic toy manufacturer uses a particular kind of quality test to check the toys.  The test indicates defects in 85% of defective toys, but it also indicates defects in 2% of nondefective toys.  The test indicates that toy A is defective.  If 5% of toys have defects, what is the probability that toy A has a defect? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58318 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=58318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An electronic toy manufacturer uses a particular kind of quality test to check the toys.  The test indicates defects in 85% of defective toys, but it also indicates defects in 2% of nondefective toys.  The test indicates that toy A is defective.  If 5% of toys have defects, what is the probability that toy A has a defect?<BR>\n" );
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document.write( "Let D be defective and D' be non defective:<BR>\n" );
document.write( "The Problem is a Bayes problem.<BR>\n" );
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document.write( "P(D) = P(D and D) + P(D and D')<BR>\n" );
document.write( "=P(D)*P(D|D) + P(D)*P(D|D')<BR>\n" );
document.write( "=P(D)[P(D|D)+P(D|D')]<BR>\n" );
document.write( "=0.05[0.85+P(D|D')]<BR>\n" );
document.write( "Need to find P(D|D')<BR>\n" );
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document.write( "P(D|D') = [P(D and D')/P(D')] = [P(D'|D)P(D)/P(D')] = [0.02*0.05/0.95]=0.0010526...<BR>\n" );
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document.write( "Put that is the P(D) line up above to get:<BR>\n" );
document.write( "P(D)=0.05[0.85+0.0010526]= 0.05(0.8510526)=0.0426<BR>\n" );
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document.write( "P(a randomly selected item is defective is defective )= 0.0426<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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