document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=267157>Question 267157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I worked the following problem can you please check it to make sure I work it right.  Thank you\r<BR>\n" );
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document.write( "If North American casino roulette were fair, how much should it pay to a player who bets $10 on red and a red number comes up? The odds against winning a bet on a red in roulette are 1.01 to 1. \r<BR>\n" );
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document.write( "If \"odds for an event (e)\" are a:b<BR>\n" );
document.write( "then P(e) = a/(a+b) P(not e) = b/(a+b)\r<BR>\n" );
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document.write( "P(winning change) 1.01/(1.01+1) = 2.1\r<BR>\n" );
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document.write( "P(winnings) 10*2.1 =21\r<BR>\n" );
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document.write( "Total winning =$21\r<BR>\n" );
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document.write( "Answer: $21.00 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196181 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=196181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If North American casino roulette were fair, how much should it pay to a player who bets $10 on red and a red number comes up? The odds against winning a bet on a red in roulette are 1.01 to 1.<BR>\n" );
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document.write( "Odds against \"e\" = P(not e)/P(e)<BR>\n" );
document.write( "If odds against red are 1.01:1<BR>\n" );
document.write( "P(not red) = 101/2.01<BR>\n" );
document.write( "P(red) = 1/2.01<BR>\n" );
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document.write( "Let \"x\" be the payoff for \"red\"<BR>\n" );
document.write( "E(x) = winnings*P(win) + loss*P(lose)<BR>\n" );
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document.write( "If the game is \"fair\" E(x) = zero<BR>\n" );
document.write( "E(x) = (x-10)(1/2.01) - 10(1.01/2.01) = 0<BR>\n" );
document.write( "Multiply thru by 2.01:<BR>\n" );
document.write( "(x-10) - 10(1.01) = 0<BR>\n" );
document.write( "x = 10(1+1.01)<BR>\n" );
document.write( "x = 10(2.01<BR>\n" );
document.write( "x = $20.10<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=====================\r<BR>\n" );
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document.write( "If \"odds for an event (e)\" are a:b<BR>\n" );
document.write( "then P(e) = a/(a+b) P(not e) = b/(a+b) <BR>\n" );
document.write( "P(winning chance) 1.01/(1.01+1) = 1.01/2.01 <BR>\n" );
document.write( "P(winnings) 10*2.01 =2.01 <BR>\n" );
document.write( "Total winning =$20.10 <BR>\n" );
document.write( "Answer: $21.10<BR>\n" );
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