document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471066>Question 471066</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One thousand raffle tickets are sold for $5.00 each. One grand prize of $800 and two consolation prizes of $100 each will be awarded. Jeremy purchases one ticket. Find his expected value. Show your work for full credit.<BR>\n" );
document.write( "  (Points : 7)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323120 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> expected value is a weighted average of all possible outcomes.<BR>\n" );
document.write( "Let p be the probability of an outcome.<BR>\n" );
document.write( "Let g be the net gain of an outcome.<BR>\n" );
document.write( "The expected value of an outcome is the product of p and g.<BR>\n" );
document.write( "E = p*g<BR>\n" );
document.write( "In this problem there are 3 outcomes: win grand prize, win consolation prize, win nothing.<BR>\n" );
document.write( "His total expected value of the raffle ticket is the sum of the expected values from each outcome.<BR>\n" );
document.write( "Outcome 1: win grand prize<BR>\n" );
document.write( "there are 1000 tickets but only 1 winner, so p = 1/1000<BR>\n" );
document.write( "you win $800 but it cost you $5, so g = 795<BR>\n" );
document.write( "Outcome 2: win consolation prize<BR>\n" );
document.write( "there are 1000 tickets and only 2 winners, so p = 2/1000 or 1/500<BR>\n" );
document.write( "you win $100 but it cost you $5, so g = 95<BR>\n" );
document.write( "Outcome 3: win nothing<BR>\n" );
document.write( "1000-2-1=997, this means 997 tickets do not win, so p = 997/1000<BR>\n" );
document.write( "you win 0 but it cost you $5, so g = -5<BR>\n" );
document.write( "Now compute Expected Value (EV):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EV+=+%281%2F1000%29%28795%29+%2B+%281%2F500%29%2895%29+%2B+%28997%2F1000%29%28-5%29 ALIGN=MIDDLE  ALT=\"EV+=+%281%2F1000%29%28795%29+%2B+%281%2F500%29%2895%29+%2B+%28997%2F1000%29%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EV+=+-4 ALIGN=MIDDLE  ALT=\"EV+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore for every raffle ticket you buy, you should expect to lose $4.<BR>\n" );
document.write( "Another way of looking at it is you expect to win $1 for every ticket you buy, but since each one costs $5 its not a very worthwhile investment. </SPAN>\n" );
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