document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725116>Question 725116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have an extra credit problem that I really need the points for. Please help me!!\r<BR>\n" );
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document.write( "A student is taking a test with several multiple choice questions. One (1) point is given for each correct.If there are 4 options for each question, and the student is penalized 1/2 point for each question wrong, how many options must he be able to rule out before the expected value of guessing is zero?\r<BR>\n" );
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document.write( "?????? Must write out work for credit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444006 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=444006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A student is taking a test with several multiple choice questions. <BR>\n" );
document.write( "One (1) point is given for each correct.<BR>\n" );
document.write( "If there are 4 options for each question, and the student is penalized 1/2 point for each question wrong, how many options must he be able to rule out before the expected value of guessing is zero? <BR>\n" );
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document.write( "Random Values:.......1......-1/2<BR>\n" );
document.write( "Probabilities:.......x.....(1-x)<BR>\n" );
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document.write( "Solve:<BR>\n" );
document.write( "E(x) = x - (1/2)(1-x) = 0<BR>\n" );
document.write( "x - (1/2) + (1/2)x = 0<BR>\n" );
document.write( "(3/2)x = 1/2<BR>\n" );
document.write( "x = (2/3)(1/2) = 1/3<BR>\n" );
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document.write( "So, if the probability of getting each problem correct is<BR>\n" );
document.write( "1/3, expected value will be zero.<BR>\n" );
document.write( "So, the student must rule out one of the options.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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