document.write( "Question 1062142: 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. \n" ); document.write( "

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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.
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This is much easier than you might think.\r\n" );
document.write( "Total number of events: \r\n" );
document.write( "The numbers you're looking for are:\r\n" );
document.write( "Doubles:\r\n" );
document.write( " 6, 8,  8\r\n" );
document.write( " 6, 6, 10\r\n" );
document.write( " 8, 8, 10\r\n" );
document.write( "2, 10, 10\r\n" );
document.write( "4, 10, 10\r\n" );
document.write( "6, 10, 10\r\n" );
document.write( "8, 10, 10

Number of ways ONE of these doubles appears in the 216 events: 
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document.write( "Now, since there are 7 DOUBLES, the number of ways those 7 doubles appear in the 216 events is: 7(3), or 21 times\r
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document.write( "Triplicates:
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document.write( " 8,  8,  8
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document.write( "10, 10, 10
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document.write( "These triple numbers ONLY appear ONCE in the 216 events, and since there are 2 of them, then they appear in 2 of the 216 events \r
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document.write( "Distincts:
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document.write( "4, 8, 10
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document.write( "6, 8, 10
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document.write( "To find the number of times each of the above numbers appears in the 216 events, we calculate: , and since there are 2 such sets, we get: 2(6), or 12
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document.write( "We now see that the number of numbers that appears with a sum > 20 is: 21 + 2 + 12.
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document.write( "So, the probability that the sum of the numbers rolled is greater than 20 =  \n" );
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