document.write( "Question 977786: Calculate the probability of throwing a pair (two of the same number) using two fair
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Algebra.Com's Answer #599360 by Edwin McCravy(20061) $\"\"$ $\"About$
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document.write( "Here are all 100 possible rolls of two 10-sided dice (computer generated):\r\n" );
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document.write( " (1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)  (1,7)  (1,8)  (1,9)  (1,10)\r\n" );
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document.write( " (2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)  (2,7)  (2,8)  (2,9)  (2,10)\r\n" );
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document.write( " (3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)  (3,7)  (3,8)  (3,9)  (3,10)\r\n" );
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document.write( " (4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)  (4,7)  (4,8)  (4,9)  (4,10)\r\n" );
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document.write( " (5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)  (5,7)  (5,8)  (5,9)  (5,10)\r\n" );
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document.write( " (6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)  (6,7)  (6,8)  (6,9)  (6,10)\r\n" );
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document.write( " (7,1)  (7,2)  (7,3)  (7,4)  (7,5)  (7,6)  (7,7)  (7,8)  (7,9)  (7,10)\r\n" );
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document.write( " (8,1)  (8,2)  (8,3)  (8,4)  (8,5)  (8,6)  (8,7)  (8,8)  (8,9)  (8,10)\r\n" );
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document.write( " (9,1)  (9,2)  (9,3)  (9,4)  (9,5)  (9,6)  (9,7)  (9,8)  (9,9)  (9,10)\r\n" );
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document.write( "(10,1) (10,2) (10,3) (10,4) (10,5) (10,6) (10,7) (10,8) (10,9) (10,10)\r\n" );
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document.write( "Look down the right to left diagonals for the number of rolls for each sum.\r\n" );
document.write( "The probabilities p(x) are the number of ways divide by 100:\r\n" );
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document.write( "                                  x     p(x)    x·p(x)\r\n" );
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document.write( "There is 1 way to get the sum     2     .01      .02\r\n" );
document.write( "There are 2 ways to get the sum   3     .02      .06\r\n" );
document.write( "There are 3 ways to get the sum   4     .03      .12\r\n" );
document.write( "There are 4 ways to get the sum   5     .04      .20\r\n" );
document.write( "There are 5 ways to get the sum   6     .05      .30\r\n" );
document.write( "There are 6 ways to get the sum   7     .06      .42\r\n" );
document.write( "There are 7 ways to get the sum   8     .07      .56\r\n" );
document.write( "There are 8 ways to get the sum   9     .08      .72\r\n" );
document.write( "There are 9 ways to get the sum  10     .09      .90\r\n" );
document.write( "There are 10 ways to get the sum 11     .10     1.10\r\n" );
document.write( "There are 9 ways to get the sum  12     .09     1.08\r\n" );
document.write( "There are 8 ways to get the sum  13     .08     1.04      \r\n" );
document.write( "There are 7 ways to get the sum  14     .07      .98\r\n" );
document.write( "There are 6 ways to get the sum  15     .06      .90\r\n" );
document.write( "There are 5 ways to get the sum  16     .05      .80\r\n" );
document.write( "There are 4 ways to get the sum  17     .04      .68\r\n" );
document.write( "There are 3 ways to get the sum  18     .03      .54\r\n" );
document.write( "There are 2 ways to get the sum  19     .02      .38\r\n" );
document.write( "There is 1 way to get the sum    20     .01      .20\r\n" );
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document.write( "                            E(X) = Σ[x·p(x)] = 11.00\r\n" );
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document.write( "Answer: 11\r\n" );
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document.write( "Edwin
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