document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134538>Question 1134538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A research team conducted a study showing that approximately 25% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)<BR>\n" );
document.write( "(a) at least one tie is too tight<BR>\n" );
document.write( "  \r<BR>\n" );
document.write( "\n" );
document.write( "(b) more than two ties are too tight<BR>\n" );
document.write( "  \r<BR>\n" );
document.write( "\n" );
document.write( "(c) no tie is too tight<BR>\n" );
document.write( "  \r<BR>\n" );
document.write( "\n" );
document.write( "(d) at least 18 ties are not too tight<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751958 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=751958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> at least one tie is 1-(no ties)<BR>\n" );
document.write( "P(no tie too tight)  is 0.75^20=0.0032 so 1-0.0032 is 0.997\r<BR>\n" );
document.write( "\n" );
document.write( "for 1 tie it is 20*.25*.75^19=0.0211<BR>\n" );
document.write( "for 2 ties it is 20C2*.0.25^2*0.75^18=0.0669<BR>\n" );
document.write( "sum of those three is 0.0922, so more than two is the complement or 0.9078 or 0.908.\r<BR>\n" );
document.write( "\n" );
document.write( "no tie is too tight is 0.0032 from above\r<BR>\n" );
document.write( "\n" );
document.write( "at least 18 are not too tight means 18, 19, 20 aren't too tight, and that means that 2, 1,0 are too tight, and that is 0.0922 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );