document.write( "Question 1184637: Suppose it costs $5.00 to roll a pair of dice. If you get paid the positive
\n" ); document.write( "difference of the two numbers in dollars that appear on the dice. What is
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Algebra.Com's Answer #815292 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here are the 36 dice rolls with 2 dice:\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
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document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
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document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
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document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
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document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
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document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "Here are the positive differences of those above:\r\n" );
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document.write( "  0     1     2     3     4     5\r\n" );
document.write( "  1     0     1     2     3     4\r\n" );
document.write( "  2     1     0     1     2     3\r\n" );
document.write( "  3     2     1     0     1     2\r\n" );
document.write( "  4     3     2     1     0     1\r\n" );
document.write( "  5     4     3     2     1     0\r\n" );
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document.write( "$X        P(X)           E(X) \r\n" );
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document.write( "$0        6/36              0\r\n" );
document.write( "$1       10/36           10/36\r\n" );
document.write( "$2        8/36           16/36 \r\n" );
document.write( "$3        6/36           18/36\r\n" );
document.write( "$4        4/36           16/36\r\n" );
document.write( "$5        2/36            2/36\r\n" );
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document.write( "     total expectation = 62/36 = 31/18 = $1.72222... \r\n" );
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document.write( "No. it isn't fair, because the expected value of the\r\n" );
document.write( "game is $1.72222... minus $5.00 = -$3.27777...\r\n" );
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document.write( "So you expect to average losing about $3.28 per game\r\n" );
document.write( "if you played the game many times.\r\n" );
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document.write( "Edwin
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