document.write( "Question 1195436: 4. A friend offers you the following game: You will roll two fair dice. If the sum of the two numbers obtained is 2, 3, 4, 9, 10, 11, or 12, your friend will pay you $20. However, if the sum of the two numbers is 5, 6, 7 or 8, you will pay your friend $20. Your friend points out that you have seven winning numbers and only four losing numbers. Is this game fair to you? Should you accept this
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Algebra.Com's Answer #827920 by ikleyn(52866)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "4. A friend offers you the following game: You will roll two fair dice.
\n" ); document.write( "If the sum of the two numbers obtained is 2, 3, 4, 9, 10, 11, or 12, your friend will pay you $20.
\n" ); document.write( "However, if the sum of the two numbers is 5, 6, 7 or 8, you will pay your friend $20.
\n" ); document.write( "Your friend points out that you have seven winning numbers and only four losing numbers.
\n" ); document.write( "Is this game fair to you? Should you accept this
\n" ); document.write( "offer? Support your conclusion with the appropriate calculation.
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document.write( "In each game, there are 6*6 = 36 possible outcomes. \r\n" );
document.write( "They are the pairs (a,b), where a and b are integer numbers from 1 to 6, inclusive,\r\n" );
document.write( "Each possible pair goes with the probability of 1/36.\r\n" );
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document.write( "P(a+b = 2) = 1/36     ( the only winning pair (a,b) is (1,1) ).\r\n" );
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document.write( "P(a+b = 3) = 2/36     ( the winning pairs (a,b) are (1,2), (2,1) ).\r\n" );
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document.write( "P(a+b = 4) = 3/36     ( the winning pairs (a,b) are (1,3), (2,2), (3,1) ).\r\n" );
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document.write( "P(a+b = 9) = 4/36     ( the winning pairs (a,b) are (3,6), (4,5), (5,4), (6,3) ).    \r\n" );
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document.write( "P(a+b = 10) = 3/36    ( the winning pairs (a,b) are (4,6), (5,5), (6,4) ).    \r\n" );
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document.write( "P(a+b = 11) = 2/36    ( the winning pairs (a,b) are (5,6), (6,5) ).    \r\n" );
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document.write( "P(a+b = 12) = 1/36    ( the only winning pair (a,b) is (6,6) ).\r\n" );
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document.write( "So, P(the sum is 2,3,4,9,10,11 or 12) = \"%281%2B2%2B3%2B4%2B3%2B2%2B1%29%2F36\" = 16/36 = 4/9.\r\n" );
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document.write( "From the other hand side, P(the sum is 5, 6, 7 or 8) is the complement to it, i.e. 1 - 4/9 = 5/9.\r\n" );
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document.write( "Thus the game is not fair: playing many time, you will lose \"%281%2F9%29%2A20\" dollars each game, in average.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On rolling dice problems see the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Rolling a pair of fair dice \r
\n" ); document.write( "\n" ); document.write( "in this site.  You will find there many similar solved problems.\r
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\n" ); document.write( "\n" ); document.write( "Read it and learn the subject from there.  After that,  you will be able easy solve such problems
\n" ); document.write( "ON  YOUR  OWN,  which is your  MAJOR  GOAL  visiting this forum  (I believe).\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic  \"Solved problems on Probability\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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