document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135509>Question 1135509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A shipment of 102 laptops contains 10 defective laptops. A quality control specialist chooses a sample of 8 laptops from the shipment.\r<BR>\n" );
document.write( "\n" );
document.write( "a) How many possible choices of 8 laptops can be made? <BR>\n" );
document.write( "b) How many of these possible selections will not contain any defective laptops?<BR>\n" );
document.write( "c) How many of the possible selections will contain at least one defective laptop?<BR>\n" );
document.write( "d) How many of the possible selections will contain exactly one defective laptop?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753173 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=753173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a is 102!/94!8! or 102C8=2.19 x 10^11 (2192950683 x 10^11) ANSWER a<BR>\n" );
document.write( "No defective ones<BR>\n" );
document.write( "92/102*91/101*90/100*89/99*88/98*87/97*86/96*85/95=0.4245 probability that none is defective so a 0.5755 probability at least one is defective.<BR>\n" );
document.write( "1-(92C8/102C8)=1.2621418 x 10^11 ANSWER c, at least one defective\r<BR>\n" );
document.write( "\n" );
document.write( "That means 9.308088718 x 10^10 ways there are no defective ones ANSWER b\r<BR>\n" );
document.write( "\n" );
document.write( "exactly one is 10C1*92C7/102C8= 0.39948 probability or 8.76056 x 10^10 ways ANSWER d<BR>\n" );
document.write( "Notice how the top part of the \"choose\" factor (hypergeometric distribution) adds to 102 and the bottom adds to 8.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );