document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018218>Question 1018218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eight of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 0f the cars have such defects. Find the probability that all 8 of the selected cars have steering defect. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634409 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=634409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "Eight of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 0f the cars have such defects. Find the probability that all 8 of the selected cars have steering defect.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "This is a problem that can be solved using the hypergeometric distribution.<BR>\n" );
document.write( "Let <BR>\n" );
document.write( "A=number of defective cars in the population<BR>\n" );
document.write( "B=number of non-defective cars in the population<BR>\n" );
document.write( "a=number of defective cars in the sample<BR>\n" );
document.write( "b=number of non-defective cars in the sample.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Then <BR>\n" );
document.write( "Probability of picking a defective out of a sample size (a+b) is<BR>\n" );
document.write( "P(a;a+b)<BR>\n" );
document.write( "=P(8;8)<BR>\n" );
document.write( "=C(A,a)*C(B,b)/C(A+B,a+b)<BR>\n" );
document.write( "=C(10,8)*C(30,0)/C(40,8)<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1708993 ALIGN=MIDDLE  ALT=\"1%2F1708993\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "This can also obtained by reasoning the long way:<BR>\n" );
document.write( "Fist defective: 10/40,<BR>\n" );
document.write( "second defective: 9/39<BR>\n" );
document.write( "...<BR>\n" );
document.write( "eighth defective: 3/33<BR>\n" );
document.write( "Multiplying together gives <BR>\n" );
document.write( "P(8,8)=10*9*8.../(40*39...33)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1708993 ALIGN=MIDDLE  ALT=\"1%2F1708993\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );