document.write( "Question 1142814: If a player rolls two dice and a gets a sum of 2 or 12, she wins $20. If a person gets a product of 12, she wins $ 15. If she gets a sum of 5 or 9, she wins $2. For the game to be fair, how much should the person pay to play the game?\r
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Algebra.Com's Answer #763548 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, and each element/event has the probability of  .\r\n" );
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document.write( "Of them, the outcomes where the sum is 2 or 12, are\r\n" );
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document.write( "    sum   2 :  (1,1)            In all, 1 pair worth $20.\r\n" );
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document.write( "    sum  12 :  (6,6)            In all, 1 pair worth $20.\r\n" );
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document.write( "The outcomes where the product is 12, are\r\n" );
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document.write( "                (2,6), (3,4), (4,3), (6,2)         In all, 4 pairs worth $15 each\r\n" );
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document.write( "The outcomes where the sum is 5 or 9, are\r\n" );
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document.write( "    sum 5 :  (1,4), (2,3), (3,2), (4,1)            In all, 4 pairs worth $2 each\r\n" );
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document.write( "    sum 9 :  (3,6), (4,5), (5,4), (6,3)            In all, 4 pairs worth $2 each\r\n" );
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document.write( "Thus the mathematical expectation of winning sum is\r\n" );
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document.write( "     =  =  =   =  dollars.\r\n" );
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document.write( "ANSWER.  For the game to be fair, the person should pay  dollars.\r\n" );
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