document.write( "Question 1131743: A card is drawn from a standard 52-card deck. Calculate the expected value for the game. A player must pay 5 dollars to play the game, which must be subtracted from the winnings. If a
\n" ); document.write( "spade is drawn, the player wins 15 dollars; otherwise, they lose their 5 dollars. Calculate the price that would make the game fair. \n" ); document.write( "

Algebra.Com's Answer #748623 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "P(spade) = 1/4; P(not spade) = 3/4.

\n" ); document.write( "Value (spade) = $10 (-$5 for playing, +$15 for winning)
\n" ); document.write( "Value (not spade) = -$5

\n" ); document.write( "Expected value of playing: $\"%281%2F4%29%2810%29%2B%283%2F4%29%28-5%29+=+10%2F4-15%2F4+=+-5%2F4\"$

\n" ); document.write( "The expected value of playing the game is -$1.25.

\n" ); document.write( "To make the game fair (make the expected value of playing equal to 0), the cost for playing the game should be x, where

\n" ); document.write( " $\"%281%2F4%29%2815-x%29%2B%283%2F4%29%28-x%29+=+0\"$
\n" ); document.write( " $\"15%2F4-%281%2F4%29x+-+%283%2F4%29x+=+0\"$
\n" ); document.write( " $\"15%2F4-x+=+0\"$
\n" ); document.write( " $\"x+=+15%2F4+=+3.75\"$

\n" ); document.write( "ANSWER: The price for playing the game, to make the game fair, should be $3.75. \n" ); document.write( "

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