document.write( "Question 1142815: Card Game. A game is set up as follows: All the diamonds are removed from a deck of cards, and these 13 cards are placed in a bag. The cards are mixed up, and then one card is chosen at random (and then replaced). The player wins according to the following rules.
\n" ); document.write( "If the ace is drawn, the player loses $20. If a face card is drawn, the player wins $10 If any other card (2-10) is drawn, the player wins $2 How much should be charged to play this game in order for it to be fair? \n" ); document.write( "

Algebra.Com's Answer #763549 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The probabilities of drawing any one of the 13 cards are all the same. So the expected value for a play is the average of the values of each card.

\n" ); document.write( "The only losing card is the ace; the player loses $20 if that card is drawn.

\n" ); document.write( "Each of the 3 face cards wins $10; each of the remaining 9 cards wins $2.

\n" ); document.write( "So the average value of each draw is

\n" ); document.write( " $\"%28%28-20%29%2B3%2810%29%2B9%282%29%29%2F13+=+%28-20%2B48%29%2F13+=+28%2F13\"$

\n" ); document.write( "On average, the player will WIN (28/13) dollars; to be a fair game, the player must PAY (28/13) dollars for a game.

\n" ); document.write( "That of course is not possible, unless the game must be played in groups of 13 draws, with a cost of $28 for the 13 draws. \n" ); document.write( "

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