document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=357303>Question 357303</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A shipment of pins contains 25 good ones and 2 defective ones. At the receiving<BR>\n" );
document.write( "department an inspector picks three pins at random and tests them. If any<BR>\n" );
document.write( "defective pin is found among the three that are tested, the shipment would be<BR>\n" );
document.write( "rejected. What is the probability that the shipment would be accepted ? To<BR>\n" );
document.write( "increase the probability of acceptance to atleast 90%, it is decided to do one of the<BR>\n" );
document.write( "following:\r<BR>\n" );
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document.write( "1. Add some good pins to the shipment<BR>\n" );
document.write( "2. Remove some defective pins in the shipment<BR>\n" );
document.write( "For each of the two options, find out exactly how many pins should be added or<BR>\n" );
document.write( "removed.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255169 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=255169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (23/25)^3=.7787  probability that the shipment would be accepted.<BR>\n" );
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document.write( "1.<BR>\n" );
document.write( "Let x = number of pins to be added to increase the probability of acceptance to atleast 90%.<BR>\n" );
document.write( "((23+x)/(25+x))^3>=.9<BR>\n" );
document.write( "((23+x)/(25+x))>=.9655... Cube root of each side.<BR>\n" );
document.write( "23+x>=.9655(25+x)<BR>\n" );
document.write( "23+x>=24.137+.9655x<BR>\n" );
document.write( ".0345x=1.137<BR>\n" );
document.write( "x>=33 pins should be added.<BR>\n" );
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document.write( "2.<BR>\n" );
document.write( "(23/24)^3=.88 one defective pin removed.<BR>\n" );
document.write( "Both defective pins would have to be removed to increase the probability of acceptance to atleast 90%.<BR>\n" );
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document.write( "Ed </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );