document.write( "Question 890015: Two fair, normal, six sided dice are used in a game of chance at the bar of the CheeseCake Restaurant. If you roll a combined value of '9' or over, you win $1.05 If you roll a '7' or '8', you lose $3. If you roll less than a '7', you win $0.60.
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\n" ); document.write( "What is your expected value if you play the game? \n" ); document.write( "

Algebra.Com's Answer #538645 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Here are all 36 rolls.\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 all the rolls with a combined value of '9' or over:\r\n" );
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document.write( "                              (3,6) \r\n" );
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document.write( "                        (4,5) (4,6) \r\n" );
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document.write( "                  (5,4) (5,5) (5,6) \r\n" );
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document.write( "            (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "There are 10 of them, so the probability of getting a roll\r\n" );
document.write( "with a combined value of '9' or over is  or \r\n" );
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document.write( "Here are the rolls of '7' or '8':\r\n" );
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document.write( "                              (1,6)\r\n" );
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document.write( "                        (2,5) (2,6) \r\n" );
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document.write( "                  (3,4) (3,5)  \r\n" );
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document.write( "            (4,3) (4,4)  \r\n" );
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document.write( "      (5,2) (5,3) \r\n" );
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document.write( "(6,1) (6,2)  \r\n" );
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document.write( "There are 11 of them, so the probability of getting a roll\r\n" );
document.write( "with a '7' or '8' is .\r\n" );
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document.write( "Here are the rolls less than a '7':\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) \r\n" );
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document.write( "(2,1) (2,2) (2,3) (2,4)  \r\n" );
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document.write( "(3,1) (3,2) (3,3)  \r\n" );
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document.write( "(4,1) (4,2)  \r\n" );
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document.write( "(5,1)  \r\n" );
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document.write( "There are 15 of them, so the probability of getting a roll\r\n" );
document.write( "less than a '7' is  or .\r\n" );
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document.write( "    Rolls    |  Probability |  Winning  |         Expectation\r\n" );
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document.write( " '9' or over |     10/36    |   $1.05   |  (10/36) ×  $1.05 =  $0.29 1/6\r\n" );
document.write( " '7' or '8'  |     11/36    |  -$3.00   |  (11/36) × -$3.00 = -$0.91 2/3 \r\n" );
document.write( "less than '7'|     15/36    |   $0.60   |  (15/36) ×  $0.60 =  $0.25\r\n" );
document.write( "------------------------------------------------------------------------\r\n" );
document.write( "Totals       |     36/36=1  |           |                     -$0.37 1/2\r\n" );
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document.write( "The expectation is  cents.  That means if you play\r\n" );
document.write( "the game many times, you will average losing  cents per game.  \r\n" );
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document.write( "Edwin

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