document.write( "Question 678873: Nonstandard dice can produce intercst- ing distributions of outcomes. Suppose you have two bal- anced, six-sided dice. Die A has faces with 2, 2, 2, 2, 6, and 6
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\n" ); document.write( "\n" ); document.write( "(a). Find a probability model for the difference (Die A - Die B) in the total number of spots on the up-faces.
\n" ); document.write( "(b). Which die is more likely to roll a higher number? Justify your answer. \n" ); document.write( "

Algebra.Com's Answer #421695 by Edwin McCravy(20056) $\"\"$ $\"About$

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(a). Find a probability model for the difference (Die A - Die B) in the total number of spots on the up-faces.
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document.write( "Here are all 36 possible rolls (A,B) with these weird dice:\r\n" );
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document.write( "(2,5)  (2,5)   (2,5)  (2,1)   (2,1)  (2,1)\r\n" );
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document.write( "(2,5)  (2,5)   (2,5)  (2,1)   (2,1)  (2,1)\r\n" );
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document.write( "(2,5)  (2,5)   (2,5)  (2,1)   (2,1)  (2,1)\r\n" );
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document.write( "(2,5)  (2,5)   (2,5)  (2,1)   (2,1)  (2,1)\r\n" );
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document.write( "(6,5)  (6,5)   (6,5)  (6,1)   (6,1)  (6,1)\r\n" );
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document.write( "(6,5)  (6,5)   (6,5)  (6,1)   (6,1)  (6,1)\r\n" );
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document.write( "Here are all the differences (Die A - Die B)\r\n" );
document.write( "in the corresponding positions to the above:\r\n" );
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document.write( " -3     -3      -3      1      1      1\r\n" );
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document.write( " -3     -3      -3      1      1      1\r\n" );
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document.write( " -3     -3      -3      1      1      1\r\n" );
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document.write( " -3     -3      -3      1      1      1\r\n" );
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document.write( "  1      1       1      5      5      5\r\n" );
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document.write( "  1      1       1      5      5      5\r\n" );
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document.write( "There are 12 -3's, 18 1's, and 6 5's.  And there\r\n" );
document.write( "are 36 possible rolls, so each probability is the\r\n" );
document.write( "number of ways to roll the difference over 36.\r\n" );
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document.write( "So we list the probablity distribution function:\r\n" );
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document.write( "(Die A - Die B)     Prob. of sum     \r\n" );
document.write( "        x               P(x)           \r\n" );
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document.write( "       -3            12/36 = 1/3           \r\n" );
document.write( "        1            18/36 = 1/2           \r\n" );
document.write( "        5             6/36 = 1/6           \r\n" );
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\n" ); document.write( "(b). Which die is more likely to roll a higher number? Justify your answer.
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document.write( "Relisting all 36 possible rolls (A,B):\r\n" );
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document.write( "(2,5)  (2,5)   (2,5)  (2,1)   (2,1)  (2,1)\r\n" );
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document.write( "(2,5)  (2,5)   (2,5)  (2,1)   (2,1)  (2,1)\r\n" );
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document.write( "(2,5)  (2,5)   (2,5)  (2,1)   (2,1)  (2,1)\r\n" );
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document.write( "(2,5)  (2,5)   (2,5)  (2,1)   (2,1)  (2,1)\r\n" );
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document.write( "(6,5)  (6,5)   (6,5)  (6,1)   (6,1)  (6,1)\r\n" );
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document.write( "(6,5)  (6,5)   (6,5)  (6,1)   (6,1)  (6,1)\r\n" );
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document.write( "We list which one shows the higher number, die A or die B,\r\n" );
document.write( "in the corresponding positions to the above rolls:\r\n" );
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document.write( "  B      B       B      A      A      A\r\n" );
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document.write( "  B      B       B      A      A      A\r\n" );
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document.write( "  B      B       B      A      A      A\r\n" );
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document.write( "  B      B       B      A      A      A\r\n" );
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document.write( "  A      A       A      A      A      A\r\n" );
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document.write( "  A      A       A      A      A      A\r\n" );
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document.write( "die A has the higher number in 24 rolls and die  \r\n" );
document.write( "B has the higher number in only 12 rolls.  So the\r\n" );
document.write( "probability that A has the higher number is 24/36\r\n" );
document.write( "or 2/3 and the probability that A has the higher\r\n" );
document.write( "number is only 12/36 or 1/3.\r\n" );
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document.write( "Edwin

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