document.write( "Question 1137809: Suppose a pair of fair dice is rolled once. Find the probability of rolling:\r
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Algebra.Com's Answer #755709 by ikleyn(52781) $\"\"$ $\"About$

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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.\r\n" );
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document.write( "Of them, the outcomes where the sum is 8 or greater, are\r\n" );
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document.write( "    sum  8 :  (2,6), (3,5), (4,4), (5,3), (6,2)     In all, 5 pairs.\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 8 or greater is  5 + 4 + 3 + 2 + 1 = 15.\r\n" );
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document.write( "Of them, the number of pairs, where at least one component is 4, is equal to 5 : (4,4), (4,5), (5,4), (4,6) and (6,4).\r\n" );
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document.write( "Starting from this point, you can find the answer to the problem's question in two ways.\r\n" );
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\n" ); document.write( "\n" ); document.write( "1-st way. \"Naive\"\r
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document.write( "The probability under the question is   = .    ANSWER\r\n" );
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document.write( "    The probability to have the sum >= 8  \r\n" );
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document.write( "        P1 = P( sum >= 8) = ;\r\n" );
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document.write( "    The probability to have the sum >= 8 AND at least one component 4  \r\n" );
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document.write( "        P2 = P(sum >= 8 AND at least one component 4) = ;\r\n" );
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document.write( "     Therefore, the conditional probability under the question is  P =  =  =  = .    ANSWER\r\n" );
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