document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198877>Question 1198877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an assembly line produces plastic piggybanks that are either pink or blue. On average, 2.4% of the banks contain defects. Of the banks with no defects, 15% were blue. The percentage of all banks produced that are perfect pink piggybanks is<BR>\n" );
document.write( "a) 82.6 b) 82.96 c) 85 d) 87.4 e) 95.2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832533 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>b) 82.96</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "========================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Work Shown:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "D = has defects<BR>\n" );
document.write( "~D = does not have defects\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B = blue<BR>\n" );
document.write( "~B = not blue, aka pink\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(D) = probability of a defect<BR>\n" );
document.write( "P(D) = 0.024<BR>\n" );
document.write( "P(~D) = probability of not a defect<BR>\n" );
document.write( "P(~D) = 1 - P(D) = 1 - 0.024 = 0.976\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(B given ~D) = probability of selecting blue, given no defects<BR>\n" );
document.write( "P(B given ~D) = 0.15<BR>\n" );
document.write( "P(B given ~D) = probability of selecting pink, given no defects<BR>\n" );
document.write( "P(~B given ~D) = 1 - P(B given ~D)<BR>\n" );
document.write( "P(~B given ~D) = 1 - 0.15<BR>\n" );
document.write( "P(~B given ~D) = 0.85\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(~B and ~D) = P(~B given ~D)*P(~D)<BR>\n" );
document.write( "P(~B and ~D) = 0.85*0.976<BR>\n" );
document.write( "P(~B and ~D) = 0.8296\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The probability of selecting a piggybank that is both pink and without defects is 0.8296<BR>\n" );
document.write( "This converts to the <font color=red>82.96%</font> after moving the decimal point two spots to the right (same as multiplying by 100).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's a way to visually represent what's going on using a tree diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=Screenshot_163.png\"><BR>\n" );
document.write( "We don't have enough information to fill out the rest of the tree; luckily, we don't need that left side at all. We simply multiply the values along the highlighted path.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );