document.write( "Question 430365: Could someone help me with this problem?
\n" ); document.write( "We are playing a dice game with 2 fair dice. You roll the dice,I will pay you $1 if the total of the dice is 6 or greater,you will pay me $3 dollars if the total of the dice is $5 or less.What is the expected value of the game for me. I know the answer is .111 but I cannot figure our how to do this problem.
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Algebra.Com's Answer #298880 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Could someone help me with this problem?
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document.write( "The other tutor has the payout and the income switched, and that's why he came\r\n" );
document.write( "up with a negative answer. \r\n" );
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document.write( "We have to find the probabilities of rolling 6 or greater and 5 or less:\r\n" );
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document.write( "Here are all the possible dice rolls with two 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( "I will color the ones red which are 6 or greater,\r\n" );
document.write( "and the one 5 or less blue:\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( "Since there are 26 red rolls above and 10 blue rolls, the probability\r\n" );
document.write( "of rolling 6 or greater is 26/36 or 13/18 and the probability of\r\n" );
document.write( "rolling 5 or less is 10/36 or 5/18\r\n" );
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document.write( "So we make a probability distribution function:\r\n" );
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document.write( "dice roll     x     p(x)\r\n" );
document.write( "6 or more     -1    13/18      \r\n" );
document.write( "5 or less     +3     5/18\r\n" );
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document.write( "E(x) = ∑[x·p(x)] = (-1)(13/18) + 3(5/18) = -13/18 + 15/18 = 2/18 = 1/9\r\n" );
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document.write( "and 1/9 as a decimal is .111···\r\n" );
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document.write( "Edwin
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