document.write( "Question 1176904: If a player rolls two dice and gets a sum of 11, he wins $ 20. if he gets a sum of 7 he wins $ 5. The cost to play the game is $ 3. Find the expectation of the game ?\r
\n" ); document.write( "\n" ); document.write( "I built a probability distribution based on gain and calculated the mean. I get an answer of $-0.39, but the key shows a different answer. Can you show me what I am doing incorrectly? \n" ); document.write( "

Algebra.Com's Answer #804958 by ikleyn(52879) $\"\"$ $\"About$

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document.write( "When rolling two dice, in all, 36 equally likely outcomes are possible.\r\n" );
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document.write( "Of them, there are 2 outcomes that produce the sum of 11 :  (5,6) and (6,5).\r\n" );
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document.write( "Also, there are 6 outcomes that produce the sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1).\r\n" );
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document.write( "So, you can win $20 with the probability    and\r\n" );
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document.write( "    you can win  $5 with the probability  .\r\n" );
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document.write( "So, your winning expectation is   =  =  = 1.94  dollars.\r\n" );
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document.write( "From it, you should subtract the cost of the play of $3,  so the expectation of the game is  $1.94 - $3.00 = - $1.06.\r\n" );
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document.write( "In other words, you will lose 1.06 dollars statistically at each game, in average.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( " - Rolling a pair of fair dice \r
\n" ); document.write( "\n" ); document.write( " - Math expectation of winning in games with rolling pair of dice \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "You will find many similar solved problems there.\r
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