document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062142>Question 1062142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three fair six-sided number cubes, each with faces labeled 0,2,4,6,8,10 are all rolled. What is the probability that the sum of the numbers rolled is greater than 20? Express your answer with a common fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676961 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676961\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at cube 1<BR>\n" );
document.write( "10<BR>\n" );
document.write( "Draw a table<BR>\n" );
document.write( "=0==2===4==6====8===10<BR>\n" );
document.write( "0<BR>\n" );
document.write( "2<BR>\n" );
document.write( "4<BR>\n" );
document.write( "6<BR>\n" );
document.write( "8<BR>\n" );
document.write( "10<BR>\n" );
document.write( "If the first cube is 10, the second and third must sum to 12 or more.  That is 2 and 10 in second row<BR>\n" );
document.write( "4, and 8 or 10 in the third row; 6 and 6,8,10 in the fourth row; 8 and 4,6,8,10 in the fifth row, and 10 and 2,4,6,8,10 in the last row.  There are 15 possibilities out of the 36 combinations or 15/36<BR>\n" );
document.write( "Multiply that by 1/6 chance first is 10, and the probability is 15/216.<BR>\n" );
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document.write( "Make the first cube 8 with 1/6 probability.<BR>\n" );
document.write( "Now the pyramid of choices that work has shifted down so instead of 1,2,3,4,5 that work, it is 1,2,3,4 or 10 possibilities.  The joint probability is 10/216<BR>\n" );
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document.write( "Make the first cube 6 with 1/6 probability and the rows that work have 1,2,3 choices or 6/36 probability.  The joint probability is 6/216.<BR>\n" );
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document.write( "Make the first cube 4 and there are only 1, 2 choices or 3/36 probability.  That is 3/216 joint probability.<BR>\n" );
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document.write( "Make the first cube 2, and there is only one choice, 10 and 10 with 1/36 probability and 1/216 joint probability.<BR>\n" );
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document.write( "If the first cube is 0, there is no chance.<BR>\n" );
document.write( "The joint probabilities sum to 15+10+6+3+1 , with denominator 216. The answer is 35/216. </SPAN>\n" );
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