document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142813>Question 1142813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A lottery offers on $1000 prize, one $500 prize and five $100 prizes.   Seven hundred tickets are sold at $4 each.  Find the expected value of a ticket if a person buys one ticket. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763550 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The solution by tutor @ikleyn shows the standard method for finding expected value, based on the definition.<br><BR>\n" );
document.write( "For this particular problem (and many similar ones), the expected value can be found much more easily.<br><BR>\n" );
document.write( "(1) The total ticket sales are 700($4) = $2800.<BR>\n" );
document.write( "(2) The total payouts are $1000 + $500 + 5($100) = $2000.<br><BR>\n" );
document.write( "The total gain by the ticket buyers is $2000-$2800 = -$800; the expected value of each one of the 700 tickets is -$800/700 = -$8/7. </SPAN>\n" );
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