Algebra.Com's Answer #844000 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Two six-sided dice are rolled and the sum is recorded.
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document.write( "Determine the probability of obtaining a sum
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document.write( "(a) a sum greater than 8
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document.write( "(b) a sum less than 6.
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document.write( " Part (a)\r\n" );
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document.write( "The full space of events is the set of all pairs (i,j), where i and j are integer numbers from 1 to 6, inclusively.\r\n" );
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document.write( "This space consists of 6*6 = 36 elements, and each element/event has the probability of  .\r\n" );
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document.write( "Of them, the outcomes where the sum is greater than 8 are\r\n" );
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document.write( " sum 9 : (3,6), (4,5), (5,4), (6,3) In all, 4 pairs.\r\n" );
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document.write( " sum 10 : (4,6), (5,5), (6,4) In all, 3 pairs.\r\n" );
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document.write( " sum 11 : (5,6), (6,5) In all, 2 pairs.\r\n" );
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document.write( " sum 12 : (6,6) Only 1 pair.\r\n" );
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document.write( "Thus the number of events where the sum is greater thsan 8 is 4 + 3 + 2 + 1 = 10.\r\n" );
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document.write( "So, the probability to have the sum of two dice greater than 8 is  =  . ANSWER to (a)\r\n" );
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document.write( " Part (b)\r\n" );
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document.write( "The full space of events is the set of all pairs (i,j), where i and j are integer numbers from 1 to 6, inclusively.\r\n" );
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document.write( "This space consists of 6*6 = 36 elements, and each element/event has the probability of .\r\n" );
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document.write( "Of them, the outcomes where the sum is less than 6 are\r\n" );
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document.write( " sum 2 : (1,1) Only 1 pair.\r\n" );
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document.write( " sum 3 : (1,2), (2,1) In all, 2 pairs.\r\n" );
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document.write( " sum 4 : (1,3), (2,2), (3,1) In all, 3 pairs.\r\n" );
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document.write( " sum 5 : (1,4), (2,3), (3,2), (4,1) In all, 4 pairs.\r\n" );
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document.write( "Thus the number of events where the sum is less than 6 is 1 + 2 + 3 + 4 = 10.\r\n" );
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document.write( "So, the probability to have the sum of two dice less than 6 is = . ANSWER to (b)\r\n" );
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document.write( "Solved.\r
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document.write( "If you want to learn this subject and this class of problems BETTER, DEEPER and WIDER, look into the lesson\r
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document.write( " - Rolling a pair of fair dice \r
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document.write( "in this site. You will find there many other similar solved problems.\r
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