document.write( "Question 871692: A pair of fair dice is rolled once. Suppose that you lose $9 if the dice sum to 10 and win $12 if the dice sum to 3 or 2. How much should you win or lose if any other number turns up in order for the game to be fair? \r
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\n" ); document.write( "\n" ); document.write( "(Do not round until the final answer.Then round to the nearest cent as needed.)
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Algebra.Com's Answer #525703 by Edwin McCravy(20065) $\"\"$ $\"About$

You can put this solution on YOUR website!

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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( "P(1 or 2) = P(green roll) = 3 ways out of 36 =  = \r\n" );
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document.write( "P(10) = P(red roll) = 3 ways out of 36 =  = \r\n" );
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document.write( "P(any other roll) = P(purple roll) = 31 ways out of 36 =  = \r\n" );
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document.write( "Roll    Probability    Winning (+)   Expectation\r\n" );
document.write( "                       or loss (-)     \r\n" );
document.write( "(X)         P(X)          W(X)        P(X)*W(X)\r\n" );
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document.write( "green       1/12          +$12            $1\r\n" );
document.write( "red         1/12           -$9          -$3/4 \r\n" );
document.write( "purple       5/6            $w          $5/6w              \r\n" );
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document.write( "                   Total expectation = $1/4 + 5/6w\r\n" );
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document.write( "For the game to be fair, the total expectation must be 0.\r\n" );
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document.write( "                          1/4 + 5/6w = 0\r\n" );
document.write( "                                5/6w = -1/4\r\n" );
document.write( "Multiply both sides by 12\r\n" );
document.write( "                                 10w = -3\r\n" );
document.write( "                                   w = -3/10 = -$.30\r\n" );
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document.write( "You should lose 30 cents if you get a purple roll.\r\n" );
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document.write( "Edwin

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