document.write( "Question 311362: A student is taking a standardized test consisting of multiple choice questions for which there are five options for each question. Seven points are awarded for each correct answer, but the student loses 2 points for an incorrect answer. Questions left blank neither receive nor lose points. What is the minimum number of options that the student should be able to rule out before making a guess on any particular question?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #222717 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
A student is taking a standardized test consisting of multiple choice questions for which there are five options for each question. Seven points are awarded for each correct answer, but the student loses 2 points for an incorrect answer. Questions left blank neither receive nor lose points. What is the minimum number of options that the student should be able to rule out before making a guess on any particular question?
\n" ); document.write( "

\r\n" );
document.write( "                                Points   Probability               \r\n" );
document.write( "Rules out 0 and guesses right     7         1/5           \r\n" );
document.write( "Rules out 0 and guesses wrong    -2         4/5\r\n" );
document.write( "\r\n" );
document.write( "Expectation = 7(1/5)+(-2)(4/5) = -1/5\r\n" );
document.write( "\r\n" );
document.write( "The expectation is negative, so one should not guess if only one\r\n" );
document.write( "option can be eliminated.\r\n" );
document.write( "\r\n" );
document.write( "                                Points   Probability           \r\n" );
document.write( "Rules out 1 and guesses right     7         1/4\r\n" );
document.write( "Rules out 0 and guesses wrong    -2         3/4\r\n" );
document.write( "\r\n" );
document.write( "Expectation = 7(1/4)+(-2)(3/4) = 1/4       \r\n" );
document.write( "\r\n" );
document.write( "Since the expected number is positive, the answer is \r\n" );
document.write( "\"If 1 option can be eliminated, then guessing is the best policy.\r\n" );
document.write( "\r\n" );
document.write( "If more options can be eliminated, then of course the best policy is to\r\n" );
document.write( "guess. I'll go thorugh the others for instructive purposes, but it really \r\n" );
document.write( "isn't nexessary.  The minimum number of options that the student should \r\n" );
document.write( "be able to rule out before making a guess is 1. \r\n" );
document.write( "\r\n" );
document.write( "                                Points   Probability           \r\n" );
document.write( "Rules out 2 and guesses right     7         1/3       \r\n" );
document.write( "Rules out 0 and guesses wrong    -2         2/3\r\n" );
document.write( "\r\n" );
document.write( "Expectation = 7(1/3)+(-2)(2/3) =  1\r\n" );
document.write( "\r\n" );
document.write( "                                Points   Probability           \r\n" );
document.write( "Rules out 3 and guesses right     7          1/2       \r\n" );
document.write( "Rules out 0 and guesses wrong    -2          1/2\r\n" );
document.write( "\r\n" );
document.write( "Expectation = 7(1/2)+(-2)(1/2) =  2.5 \r\n" );
document.write( "\r\n" );
document.write( "                                 Points   Probability\r\n" );
document.write( "Rules out 4 and guesses right     7           1       \r\n" );
document.write( "Rules out 0 and guesses wrong    -2           0\r\n" );
document.write( "\r\n" );
document.write( "Expectation = 7(1)+(-2)(0) =  7 \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );