document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103446>Question 1103446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A) We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected value?\r<BR>\n" );
document.write( "\n" );
document.write( "B)What is the price that you should pay to play the game that would make the game fair?<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 #718143 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=718143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The expected value is found by adding all the products of the probability of each outcome and the value of each outcome.<br><BR>\n" );
document.write( "1/36 probability of getting a 2; 2*1/36 = 2/36<BR>\n" );
document.write( "2/36 probability of getting a 3; 3*2/36 = 6/36<BR>\n" );
document.write( "3/36 probability of getting a 4; 4*3/36 = 12/36<BR>\n" );
document.write( "4/36 probability of getting a 5; 5*4/36 = 20/36<BR>\n" );
document.write( "5/36 probability of getting a 6; 6*5/36 = 30/36<BR>\n" );
document.write( "6/36 probability of getting a 7; 7*-30/36 = -210/36<BR>\n" );
document.write( "5/36 probability of getting a 8; 8*5/36 = 40/36<BR>\n" );
document.write( "4/36 probability of getting a 9; 9*4/36 = 36/36<BR>\n" );
document.write( "3/36 probability of getting a 10; 10*3/36 = 30/36<BR>\n" );
document.write( "2/36 probability of getting a 11; 11*2/36 = 22/36<BR>\n" );
document.write( "1/36 probability of getting a 12; 12*1/36 = 12/36<br><BR>\n" );
document.write( "The expected value is the sum of all those fractions, which is exactly 0.<br><BR>\n" );
document.write( "So the game is fair at the current price. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );