document.write( "Question 474884: A game involves tossing two coins. A player wins $1.00 if both tosses result in heads. What should you pay to play this game in order to make it a fair game? Explain your answer. \n" ); document.write( "
Algebra.Com's Answer #325691 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You'll win ¼ of the time so you should pay ¼ of a dollar \r\n" );
document.write( "or 25 cents to break even in the long run.  But here is \r\n" );
document.write( "the work:\r\n" );
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document.write( "Let y be the amount to pay\r\n" );
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document.write( "    Coin     Winnings     Probability    Expectation\r\n" );
document.write( "   tosses    or losses     of this        per game  \r\n" );
document.write( "                X            P(X)         X·P(X)\r\n" );
document.write( "   ---------------------------------------------\r\n" );
document.write( "     HH       $1-y            ¼         (1-y)(¼)   \r\n" );
document.write( "     HT         -y            ¼            -y(¼) \r\n" );
document.write( "     TH         -y            ¼            -y(¼)\r\n" );
document.write( "     TT         -y            ¼            -y(¼)\r\n" );
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document.write( "         Sum of expectations = 0\r\n" );
document.write( "(1-y)(¼) - y(¼) - y(¼) -y(¼) = 0\r\n" );
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document.write( "Multiply through by 4\r\n" );
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document.write( "  (1-y) - y - y - y = 0\r\n" );
document.write( "  1 - y - y - y - y = 0\r\n" );
document.write( "             1 - 4y = 0\r\n" );
document.write( "                -4y = -1\r\n" );
document.write( "                  y = ¼ = .25 = 25 cents\r\n" );
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document.write( " Edwin
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