document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269461>Question 269461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a student randomly guesses at 20 multiple choice questions, find the probability that the student gets exactly four right. Each answer has four possible choices.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197499 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=197499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you want 4 correct and 16 incorrect<BR>\n" );
document.write( "there are 20 questions<BR>\n" );
document.write( "each question has four answers, so <BR>\n" );
document.write( "P(right answer) = 1/4<BR>\n" );
document.write( "P(wrong answer) = 3/4<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Since you want 4 correct of 20 we have a combination of 20C4<BR>\n" );
document.write( "This is a binomial problem where p = 1/4, q = 3/4 and we get<BR>\n" );
document.write( "(20 \"choose\" 4)*(probability correct)^(number correct)*(probability incorrect)^(number incorrect)<BR>\n" );
document.write( "putting numbers in we get<BR>\n" );
document.write( "(20c4)*(1/4)^4*(3/4)^16<BR>\n" );
document.write( "This gives us<BR>\n" );
document.write( "~ .189685 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );