document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358806>Question 358806</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A lottery has one $2000 prize, two $1000 prizes, and ten $500 prizes. Two thousand tickets are sold at $5 each. Find the expectation if a person buys two tickets? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256086 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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/cgi-bin/show-face.mpl?user=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=256086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> expectation is the same as the long term average value.\r<BR>\n" );
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document.write( "values are the net return<BR>\n" );
document.write( "2000-5=1995<BR>\n" );
document.write( "1000-5=995<BR>\n" );
document.write( "500-5=495<BR>\n" );
document.write( "-5=-5<BR>\n" );
document.write( "you subtract 5 because the is the cost of playing and you dont get that back<BR>\n" );
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document.write( "each of these occur with prob<BR>\n" );
document.write( "1/2000<BR>\n" );
document.write( "2/2000<BR>\n" );
document.write( "10/2000<BR>\n" );
document.write( "1987/2000<BR>\n" );
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document.write( "so the expected value or long term average is sum (value*prob)<BR>\n" );
document.write( "=1995*(1/2000)+995*(2/2000)+495*(10/2000)+(-5)*(1987/2000)=-0.50 so on average you loose 0.50 for each ticket.  If you buy 2 tickets your long term average is a loss of -1.00 dollar. </SPAN>\n" );
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