document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=294546>Question 294546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You roll two dice.  What is the probability that you will roll a combination where the difference is less than two? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212531 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=212531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do you mean absolute value of the difference or not? <BR>\n" );
document.write( "We'll do it both ways. <BR>\n" );
document.write( "There are 36 possible outcomes for the roll of two die. <BR>\n" );
document.write( "Here are the outcomes and the absolute value of the difference.<BR>\n" );
document.write( "1 1 0<BR>\n" );
document.write( "1 2 1<BR>\n" );
document.write( "1 3 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( ". <BR>\n" );
document.write( ".<BR>\n" );
document.write( "6 5 1<BR>\n" );
document.write( "6 6 0<BR>\n" );
document.write( "When you look at all of the occurences you get, <BR>\n" );
document.write( "0, 6 outcomes<BR>\n" );
document.write( "1, 10 outcomes<BR>\n" );
document.write( "2,8 outcomes<BR>\n" );
document.write( "3,6 outcomes<BR>\n" );
document.write( "4,4 outcomes<BR>\n" );
document.write( "5,2 outcomes<BR>\n" );
document.write( "Less than two, that's the total of 0 and 1 which is 16 outcomes.<BR>\n" );
document.write( "P(diff<2)=16/36=4/9.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If we don't use absolute value,<BR>\n" );
document.write( "1 1 0<BR>\n" );
document.write( "1 2 -1<BR>\n" );
document.write( "1 3 -2<BR>\n" );
document.write( ".<BR>\n" );
document.write( ". <BR>\n" );
document.write( ".<BR>\n" );
document.write( "6 5 1<BR>\n" );
document.write( "6 6 0<BR>\n" );
document.write( "When you look at all of the occurences you get, <BR>\n" );
document.write( "-5	,1 outcomes<BR>\n" );
document.write( "-4	,2 outcomes<BR>\n" );
document.write( "-3	,3 outcomes<BR>\n" );
document.write( "-2	,4 outcomes<BR>\n" );
document.write( "-1	,5 outcomes<BR>\n" );
document.write( "0	,6 outcomes<BR>\n" );
document.write( "1	,5 outcomes<BR>\n" );
document.write( "2	,4 outcomes<BR>\n" );
document.write( "3	,3 outcomes<BR>\n" );
document.write( "4	,2 outcomes<BR>\n" );
document.write( "5	,1 outcomes<BR>\n" );
document.write( "Less than 2, would be from -5 to 1, for a total of 1+2+3+4+5+6+5=26 outcomes<BR>\n" );
document.write( "P(diff<2)=26/36=13/18. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );