document.write( "Question 274643: a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair? \n" ); document.write( "

Algebra.Com's Answer #200409 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair?
\n" ); document.write( "------------------------------
\n" ); document.write( "Let the cost to play be \"x\" dollars.
\n" ); document.write( "-------------------------------
\n" ); document.write( "Random gain values: 5-x ; 2-x ; -x
\n" ); document.write( "Probabilities::::: 8/52 ; 13/52 ; 31/52
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "Note: If the game is fair expected gain should be zero.
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "Equation:
\n" ); document.write( "E(x) = (8/52)(5-x) + (13/52)(2-x) + (31/52)x = 0
\n" ); document.write( "----------
\n" ); document.write( "Multiply thru by 52 to get:
\n" ); document.write( "[40 - 8x + 26 - 13x + 31x) = 0
\n" ); document.write( "10x - 66 = 0
\n" ); document.write( "x = $6.60 (amount you should pay to play the game)
\n" ); document.write( "=====================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

\n" );