document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128750>Question 1128750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mark draws one card from a standard deck of 52. He receives $0.50 for a heart and $0.70 for an ace, but $0.75 for the ace of hearts. How much could he pay to play this game per draw if he expects to break even in the long run? </SPAN>\n" );
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document.write( "His expected payouts and the corresponding probabilities are<br><BR>\n" );
document.write( "$0.75 * (1/52) for the ace of hearts<BR>\n" );
document.write( "$0.70 * (3/52) for any of the other aces<BR>\n" );
document.write( "$0.50 * (12/52) for any of the other hearts<BR>\n" );
document.write( "$0.00 * 36/52) for any of the other cards<br><BR>\n" );
document.write( "His total expected payout is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.75%281%2F52%29%2B.70%283%2F52%29%2B.50%2812%2F52%29+=+8.85%2F52 ALIGN=MIDDLE  ALT=\".75%281%2F52%29%2B.70%283%2F52%29%2B.50%2812%2F52%29+=+8.85%2F52\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 17.01923 to 5 decimal places.<br><BR>\n" );
document.write( "So he can't realistically expect to EXACTLY break even.  If he pays $0.17 to play the game, then in the long run he can expect to come out very slightly ahead. </SPAN>\n" );
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