document.write( "Question 739730: A certain game involves tossing 3 fair coins, and it pays 10 cents for 3 head, 5 cents for 2 heads, and 3 cents for 1 head. Is 5 cents a fair price to pay to play this game ? (That is, does the 5 cents cost to play make the game fair?) \n" ); document.write( "

Algebra.Com's Answer #451332 by Edwin McCravy(20056) $\"\"$ $\"About$

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A certain game involves tossing 3 fair coins, and it pays 10 cents for 3 head, 5 cents for 2 heads, and 3 cents for 1 head. Is 5 cents a fair price to pay to play this game ? (That is, does the 5 cents cost to play make the game fair?)
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document.write( "First we determine the various probabilities\r\n" );
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document.write( "TOSS   P(TOSS)   Number of heads\r\n" );
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document.write( "HHH     1/8           3\r\n" );
document.write( "HHT     1/8           2\r\n" );
document.write( "HTH     1/8           2\r\n" );
document.write( "HTT     1/8           1\r\n" );
document.write( "THH     1/8           2\r\n" );
document.write( "THT     1/8           1\r\n" );
document.write( "TTH     1/8           1\r\n" );
document.write( "TTT     1/8           0\r\n" );
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document.write( "Then we make this chart:\r\n" );
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document.write( "Number of heads   Prob   Winning   Expectation\r\n" );
document.write( "       x            p      \r\n" );
document.write( "       3          1/8      10¢      (1/8)10¢ = 1.25¢\r\n" );
document.write( "       2          3/8       5¢      (3/8)5¢ =  1.875¢\r\n" );
document.write( "       1          3/8       3¢      (3/8)3¢ =  1.125¢ \r\n" );
document.write( "       0          1/8       0¢      (1/8)0¢ =  0¢ \r\n" );
document.write( "                                  ---------------------\r\n" );
document.write( "                                 Total expectation = 4.25¢\r\n" );
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document.write( "So if you played this game many times you would average \r\n" );
document.write( "getting 4.25¢ per time you played.\r\n" );
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document.write( "So if you paid a nickel to play, you would average losing\r\n" );
document.write( "0.75¢ per game, (three-fourths of a penny!) so it would not be fair.\r\n" );
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document.write( "Edwin

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