document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110074>Question 1110074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Supposed a certain game is fair and costs $8 if you lose and has a net payoff of $4 if you win. The only possible outcomes of the game are winning and losing.\r<BR>\n" );
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document.write( "What is the probability of winning? </SPAN>\n" );
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document.write( "A fair game means you break even after several games.  Just looking at the numbers, it takes 2 wins at $4 each to balance 1 loss at -$8.  So you need to win 2 out of every 3 games to break even.  That makes the probability of winning 2/3.<br><BR>\n" );
document.write( "Formally, you want the expected value of a game to be 0.  If the probability of winning is x, then the probability of losing is (1-x); for the expected value to be 0, we need to have<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-8+=+0 ALIGN=MIDDLE  ALT=\"12x-8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x+=+8 ALIGN=MIDDLE  ALT=\"12x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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