document.write( "Question 293874: If 3 dice are rolled at the same time, what is the probability of all 3 dice showing even face
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Algebra.Com's Answer #212052 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
If 3 dice are rolled at the same time, what is the probability of all 3 dice showing even face
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document.write( "We calculate the numerator of the desired probability:\r\n" );
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document.write( "There are 3 ways an even number can show up on the first die\r\n" );
document.write( "AND\r\n" );
document.write( "There are 3 ways an even number can show up on the second die\r\n" );
document.write( "AND\r\n" );
document.write( "There are 3 ways an even number can show up on the third die\r\n" );
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document.write( "So since \"AND\" means \"MULTIPLY\", there are 3x3x3 or 27 ways\r\n" );
document.write( "the three dice can all come up even.  So the numerator of\r\n" );
document.write( "the probability is 27.\r\n" );
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document.write( "We calculate the denominator of the desired probability:\r\n" );
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document.write( "There are 6 ways any number can show up on the first die\r\n" );
document.write( "AND\r\n" );
document.write( "There are 6 ways any number can show up on the second die\r\n" );
document.write( "AND\r\n" );
document.write( "There are 6 ways any number can show up on the third die\r\n" );
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document.write( "So since \"AND\" means \"MULTIPLY\", there are 6x6x6 or 216 ways\r\n" );
document.write( "the three dice can all come up any number.  So the denominator\r\n" );
document.write( "of the probability is 216.\r\n" );
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document.write( "Therefore the desired probability is \"27%2F216\" or \"1%2F8\"\r\n" );
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document.write( "Below is the sample space of all 216 outcomes, and the 27 red \r\n" );
document.write( "ones are the successful outcomes. \r\n" );
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document.write( "(1,1,1)  (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)\r\n" );
document.write( "(1,2,1)  (1,2,2)  (1,2,3)  (1,2,4)  (1,2,5)  (1,2,6)\r\n" );
document.write( "(1,3,1)  (1,3,2)  (1,3,3)  (1,3,4)  (1,3,5)  (1,3,6)\r\n" );
document.write( "(1,4,1)  (1,4,2)  (1,4,3)  (1,4,4)  (1,4,5)  (1,4,6)\r\n" );
document.write( "(1,5,1)  (1,5,2)  (1,5,3)  (1,5,4)  (1,5,5)  (1,5,6)\r\n" );
document.write( "(1,6,1)  (1,6,2)  (1,6,3)  (1,6,4)  (1,6,5)  (1,6,6)\r\n" );
document.write( "(2,1,1)  (2,1,2)  (2,1,3)  (2,1,4)  (2,1,5)  (2,1,6)\r\n" );
document.write( "(2,2,1)  (2,2,2)  (2,2,3)  (2,2,4)  (2,2,5)  (2,2,6)\r\n" );
document.write( "(2,3,1)  (2,3,2)  (2,3,3)  (2,3,4)  (2,3,5)  (2,3,6)\r\n" );
document.write( "(2,4,1)  (2,4,2)  (2,4,3)  (2,4,4)  (2,4,5)  (2,4,6)\r\n" );
document.write( "(2,5,1)  (2,5,2)  (2,5,3)  (2,5,4)  (2,5,5)  (2,5,6)\r\n" );
document.write( "(2,6,1)  (2,6,2)  (2,6,3)  (2,6,4)  (2,6,5)  (2,6,6)\r\n" );
document.write( "(3,1,1)  (3,1,2)  (3,1,3)  (3,1,4)  (3,1,5)  (3,1,6)\r\n" );
document.write( "(3,2,1)  (3,2,2)  (3,2,3)  (3,2,4)  (3,2,5)  (3,2,6)\r\n" );
document.write( "(3,3,1)  (3,3,2)  (3,3,3)  (3,3,4)  (3,3,5)  (3,3,6)\r\n" );
document.write( "(3,4,1)  (3,4,2)  (3,4,3)  (3,4,4)  (3,4,5)  (3,4,6)\r\n" );
document.write( "(3,5,1)  (3,5,2)  (3,5,3)  (3,5,4)  (3,5,5)  (3,5,6)\r\n" );
document.write( "(3,6,1)  (3,6,2)  (3,6,3)  (3,6,4)  (3,6,5)  (3,6,6)\r\n" );
document.write( "(4,1,1)  (4,1,2)  (4,1,3)  (4,1,4)  (4,1,5)  (4,1,6)\r\n" );
document.write( "(4,2,1)  (4,2,2)  (4,2,3)  (4,2,4)  (4,2,5)  (4,2,6)\r\n" );
document.write( "(4,3,1)  (4,3,2)  (4,3,3)  (4,3,4)  (4,3,5)  (4,3,6)\r\n" );
document.write( "(4,4,1)  (4,4,2)  (4,4,3)  (4,4,4)  (4,4,5)  (4,4,6)\r\n" );
document.write( "(4,5,1)  (4,5,2)  (4,5,3)  (4,5,4)  (4,5,5)  (4,5,6)\r\n" );
document.write( "(4,6,1)  (4,6,2)  (4,6,3)  (4,6,4)  (4,6,5)  (4,6,6)\r\n" );
document.write( "(5,1,1)  (5,1,2)  (5,1,3)  (5,1,4)  (5,1,5)  (5,1,6)\r\n" );
document.write( "(5,2,1)  (5,2,2)  (5,2,3)  (5,2,4)  (5,2,5)  (5,2,6)\r\n" );
document.write( "(5,3,1)  (5,3,2)  (5,3,3)  (5,3,4)  (5,3,5)  (5,3,6)\r\n" );
document.write( "(5,4,1)  (5,4,2)  (5,4,3)  (5,4,4)  (5,4,5)  (5,4,6)\r\n" );
document.write( "(5,5,1)  (5,5,2)  (5,5,3)  (5,5,4)  (5,5,5)  (5,5,6)\r\n" );
document.write( "(5,6,1)  (5,6,2)  (5,6,3)  (5,6,4)  (5,6,5)  (5,6,6)\r\n" );
document.write( "(6,1,1)  (6,1,2)  (6,1,3)  (6,1,4)  (6,1,5)  (6,1,6)\r\n" );
document.write( "(6,2,1)  (6,2,2)  (6,2,3)  (6,2,4)  (6,2,5)  (6,2,6)\r\n" );
document.write( "(6,3,1)  (6,3,2)  (6,3,3)  (6,3,4)  (6,3,5)  (6,3,6)\r\n" );
document.write( "(6,4,1)  (6,4,2)  (6,4,3)  (6,4,4)  (6,4,5)  (6,4,6)\r\n" );
document.write( "(6,5,1)  (6,5,2)  (6,5,3)  (6,5,4)  (6,5,5)  (6,5,6)\r\n" );
document.write( "(6,6,1)  (6,6,2)  (6,6,3)  (6,6,4)  (6,6,5)  (6,6,6)\r\n" );
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document.write( "------------------------------\r\n" );
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\n" ); document.write( "If 2 dice are rolled at the same time, what is the probability of the 2 dice having the same face value?
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document.write( "We calculate the numerator of the desired probability:\r\n" );
document.write( "\r\n" );
document.write( "There are 6 ways any number can show up on the first die\r\n" );
document.write( "AND\r\n" );
document.write( "There is only 1 way that same number can show up on the second die\r\n" );
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document.write( "So since \"AND\" means \"MULTIPLY\", there are 6x1 or 6 ways\r\n" );
document.write( "that both dice can come up the same.  So the numerator of\r\n" );
document.write( "the probability is 6.\r\n" );
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document.write( "We calculate the denominator of the desired probability:\r\n" );
document.write( "\r\n" );
document.write( "There are 6 ways any number can show up on the first die\r\n" );
document.write( "AND\r\n" );
document.write( "There are 6 ways any number can show up on the second die\r\n" );
document.write( "\r\n" );
document.write( "So since \"AND\" means \"MULTIPLY\", there are 6x6 or 36 ways\r\n" );
document.write( "the two dice can all come up any number.  So the denominator\r\n" );
document.write( "of the probability is 36.\r\n" );
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document.write( "Therefore the desired probability is \"6%2F36\" or \"1%2F6\"\r\n" );
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document.write( "Below is the sample space of all 36 outcomes, and the 6 red \r\n" );
document.write( "ones are the successful outcomes.\r\n" );
document.write( "\r\n" );
document.write( "(1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)\r\n" );
document.write( "(2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)\r\n" );
document.write( "(3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)\r\n" );
document.write( "(4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)\r\n" );
document.write( "(5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)\r\n" );
document.write( "(6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)\r\n" );
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document.write( "Edwin
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