document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199367>Question 1199367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The (simplified) probability of losing this bet is 47/54.<BR>\n" );
document.write( "If a player bets $18 on the $5 denomination, find the player's expectation. (Round your answer to two decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848460 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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=848460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate the Probability of Winning:**\r<BR>\n" );
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document.write( "* Probability of winning = 1 - Probability of losing <BR>\n" );
document.write( "* Probability of winning = 1 - (47/54) = 7/54\r<BR>\n" );
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document.write( "**2. Calculate the Expected Value**\r<BR>\n" );
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document.write( "* Expected Value = (Probability of Winning * Winnings) - (Probability of Losing * Bet Amount)<BR>\n" );
document.write( "* Expected Value = (7/54 * $5) - (47/54 * $18) <BR>\n" );
document.write( "* Expected Value = ($35/54) - ($846/54)<BR>\n" );
document.write( "* Expected Value = -$811/54 <BR>\n" );
document.write( "* Expected Value ≈ -$15.02\r<BR>\n" );
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document.write( "**Therefore, the player's expected value of this bet is -$15.02.** This means, on average, the player can expect to lose $15.02 for each $18 bet.<BR>\n" );
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