document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200328>Question 1200328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person must pay $4 to play a certain game at the casino. Each player has a probability of 0.12 of winning $15, for a net gain of $11 (the net gain is the amount won 15 minus the cost of playing 4).\r<BR>\n" );
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document.write( "Each player has a probability of 0.88 of losing the game, for a net loss of $4 (the net loss is simply the cost of playing since nothing else is lost).\r<BR>\n" );
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document.write( "What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the \"-\" sign with the answer. Express the answer with two decimal places.\r<BR>\n" );
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document.write( "Expected Value = $ \r<BR>\n" );
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document.write( "If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834439 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "X = net winnings from the player's perspective\r<BR>\n" );
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document.write( "We start off with this probability distribution<BR>\n" );
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document.write( "<tr><TD >X</TD><TD >P(X)</TD></tr><tr><TD >11</TD><TD >0.12</TD></tr><tr><TD >-4</TD><TD >0.88</TD></tr>\n" );
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document.write( "Let's introduce a third column labeled X*P(X)<BR>\n" );
document.write( "We'll multiply each X and P(X) value along a given row.<BR>\n" );
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document.write( "<tr><TD >X</TD><TD >P(X)</TD><TD >X*P(X)</TD></tr><tr><TD >11</TD><TD >0.12</TD><TD >1.32</TD></tr><tr><TD >-4</TD><TD >0.88</TD><TD >-3.52</TD></tr>\n" );
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document.write( "Add up the values in that third column<BR>\n" );
document.write( "1.32 + (-3.52) = -2.20<BR>\n" );
document.write( "The player expects to lose $2.20 on average per game.\r<BR>\n" );
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document.write( "Over the course of a large number of games, the player is expected to lose a lot of money.<BR>\n" );
document.write( "For instance, if s/he plays 1000 games, then that player is expected to lose around 2200 dollars (since 2.2*1000 = 2200). This is an average.<BR>\n" );
document.write( "This makes sense because the odds are rigged in favor of the casino. Otherwise the casino wouldn't make any money. \r<BR>\n" );
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document.write( "Answer: Expected value = <font color=red size=4>-2.20</font><BR>\n" );
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