document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033163>Question 1033163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mrs. Hudson plans to give a 10 question multiple choice exam in which each question has 4 options. Each question counts for 1 point.  A score of 8 or more is a passing score while 7 or less is a failing score.   The probabilities of guessing a certain number of questions correctly are listed in the table below. <BR>\n" );
document.write( "Number of Questions Correct<BR>\n" );
document.write( "Probability for Guessing Correctly<BR>\n" );
document.write( "0<BR>\n" );
document.write( "0.05631351<BR>\n" );
document.write( "1<BR>\n" );
document.write( "0.18771172<BR>\n" );
document.write( "2<BR>\n" );
document.write( "0.28156757<BR>\n" );
document.write( "3<BR>\n" );
document.write( "0.25028229<BR>\n" );
document.write( "4<BR>\n" );
document.write( "0.14599800<BR>\n" );
document.write( "5<BR>\n" );
document.write( "0.05839920<BR>\n" );
document.write( "6<BR>\n" );
document.write( "0.01622200<BR>\n" );
document.write( "7<BR>\n" );
document.write( "0.00308990<BR>\n" );
document.write( "8<BR>\n" );
document.write( "0.00038624<BR>\n" );
document.write( "9<BR>\n" );
document.write( "0.00002861<BR>\n" );
document.write( "10<BR>\n" );
document.write( "0.00000095<BR>\n" );
document.write( " <BR>\n" );
document.write( "I. Compute the probability of answering 8 or more questions correctly by calculating the probability with a direct sum and by using complements.<BR>\n" );
document.write( "How do the two approaches compare?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647814 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Direct sum<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X%3E=8%29=P%288%29%2BP%289%29%2BP%2810%29 ALIGN=MIDDLE  ALT=\"P%28X%3E=8%29=P%288%29%2BP%289%29%2BP%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Complement<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X%3E=8%29=1-P%28X%3C8%29=1-P%281%29-P%282%29-P%283%29-P%284%29-P%285%29-P%286%29-P%287%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Direct sum has fewer terms. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );