document.write( "Question 360489: Three six sided dice are thrown and produce a random set of numbers
\n" ); document.write( "eg 1 4 6 = 11.\r
\n" ); document.write( "\n" ); document.write( "Now a second set of three six sided dice are thrown.\r
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\n" ); document.write( "\n" ); document.write( "Before any dice are thrown including the first set what is the probability that the sum total for both dice set A will be equal to the sum total of dice set B
\n" ); document.write( "before we know the result of A.\r
\n" ); document.write( "\n" ); document.write( "MIke Manttan\r
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\n" ); document.write( "\n" ); document.write( "sets will be exactly equal. Not just 11 but any number \n" ); document.write( "
Algebra.Com's Answer #257274 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "3 dice can fall in exactly 63 or 216 ways.  \r\n" );
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document.write( "3 dice can have sum 3 in exactly 1 way.\r\n" );
document.write( "3 dice can have sum 4 in exactly 3 ways.\r\n" );
document.write( "3 dice can have sum 5 in exactly 6 ways.\r\n" );
document.write( "3 dice can have sum 6 in exactly 10 ways.\r\n" );
document.write( "3 dice can have sum 7 in exactly 15 ways.\r\n" );
document.write( "3 dice can have sum 8 in exactly 21 ways.\r\n" );
document.write( "3 dice can have sum 9 in exactly 25 ways.\r\n" );
document.write( "3 dice can have sum 10 in exactly 27 ways.\r\n" );
document.write( "3 dice can have sum 11 in exactly 27 ways.\r\n" );
document.write( "3 dice can have sum 12 in exactly 25 ways.\r\n" );
document.write( "3 dice can have sum 13 in exactly 21 ways.\r\n" );
document.write( "3 dice can have sum 14 in exactly 15 ways.\r\n" );
document.write( "3 dice can have sum 15 in exactly 10 ways.\r\n" );
document.write( "3 dice can have sum 16 in exactly 6 ways.\r\n" );
document.write( "3 dice can have sum 17 in exactly 3 ways.\r\n" );
document.write( "3 dice can have sum 18 in exactly 1 way.\r\n" );
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document.write( "Note that 1+3+6+10+15+21+25+27+27+25+21+15+10+5+3+1 = 216 = 63.\r\n" );
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document.write( "So there are 216×216 or 46656 ways both sets of dice can fall.\r\n" );
document.write( "That will be the denominator of the desired probability.\r\n" );
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document.write( "The number of ways both sets of dice can have sum 3 is 1×1 or 1.\r\n" );
document.write( "The number of ways both sets of dice can have sum 4 is 3×3 or 9.\r\n" );
document.write( "The number of ways both sets of dice can have sum 5 is 6×6 or 36.\r\n" );
document.write( "The number of ways both sets of dice can have sum 6 is 10×10 or 100.\r\n" );
document.write( "The number of ways both sets of dice can have sum 7 is 15×15 or 225.\r\n" );
document.write( "The number of ways both sets of dice can have sum 8 is 21×21 or 441.\r\n" );
document.write( "The number of ways both sets of dice can have sum 9 is 25×25 or 625.\r\n" );
document.write( "The number of ways both sets of dice can have sum 10 is 27×27 or 729.\r\n" );
document.write( "The number of ways both sets of dice can have sum 11 is 27×27 or 729.\r\n" );
document.write( "The number of ways both sets of dice can have sum 12 is 25×25 or 625.\r\n" );
document.write( "The number of ways both sets of dice can have sum 13 is 21×21 or 441.\r\n" );
document.write( "The number of ways both sets of dice can have sum 14 is 15×15 or 225.\r\n" );
document.write( "The number of ways both sets of dice can have sum 15 is 10×10 or 100.\r\n" );
document.write( "The number of ways both sets of dice can have sum 16 is 6×6 or 36.\r\n" );
document.write( "The number of ways both sets of dice can have sum 17 is 3×3 or 9.\r\n" );
document.write( "The number of ways both sets of dice can have sum 18 is 1×1 or 1.\r\n" );
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document.write( "1+9+36+100+225+441+625+729+729+625+441+225+100+36+9+1 = 4332\r\n" );
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document.write( "Therefore the desired probability is \"4332%2F46656\" = \"361%2F3888\"\r\n" );
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document.write( "or about 0.0928497942\r\n" );
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document.write( "Edwin
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