document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195253>Question 1195253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MD has a new type of scratch-off ticket for $500 to win one of:\r<BR>\n" );
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document.write( "10 prizes of $700<BR>\n" );
document.write( "2 runner-up prizes of $3,000<BR>\n" );
document.write( "1 grand prize of $600,000<BR>\n" );
document.write( "Once they’ve sold 5,000 tickets, they will select the winning tickets. \r<BR>\n" );
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document.write( "What is the expected value? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827678 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=827678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The question is presumably the expected value OF ONE TICKET....<br><BR>\n" );
document.write( "(1) Using the formal definition of expected value....<br><BR>\n" );
document.write( "Cost: $500<BR>\n" );
document.write( "10/5000 chance of winning $700<BR>\n" );
document.write( "2/5000 chance of winning $3000<BR>\n" );
document.write( "1/5000 chance of winning $600,000<br><BR>\n" );
document.write( "Expected value:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2F5000%29%28700%29%2B%282%2F5000%29%283000%29%2B%281%2F5000%29%28600000%29-500 ALIGN=MIDDLE  ALT=\"%2810%2F5000%29%28700%29%2B%282%2F5000%29%283000%29%2B%281%2F5000%29%28600000%29-500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.4%2B1.2%2B120%29-500 ALIGN=MIDDLE  ALT=\"%281.4%2B1.2%2B120%29-500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=122.6-500 ALIGN=MIDDLE  ALT=\"122.6-500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-377.4 ALIGN=MIDDLE  ALT=\"-377.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: -377.4; or a loss of $377.40<br><BR>\n" );
document.write( "(2) Using a less formal common sense method (which uses the same calculations, though in a different order)....<br><BR>\n" );
document.write( "Total payout: 10($700)+2($3000)+1($600,000) = $613,000<BR>\n" );
document.write( "Total cost of the 500 tickets: 5000($500) = $2,500,000<BR>\n" );
document.write( "payout minus cost: -$1,887,000<br><BR>\n" );
document.write( "expected value per ticket: (-$1,887,000)/5000 = -$377.40<br><BR>\n" );
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