document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142582>Question 1142582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a local symphony decides to raise money by raffling off a microwave oven<BR>\n" );
document.write( "worth $200, a dinner for two worth $100, and 4 books worth $20 each, total of 1000<BR>\n" );
document.write( "tickets are sold at $1 each. Find the expected value of winning for a person who buys<BR>\n" );
document.write( "1 ticket in the raffle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763261 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</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=763261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "--------------------------------------------------------------<br><BR>\n" );
document.write( "Response edited after re-reading the problem as having one $100 prize instead of two<br><BR>\n" );
document.write( "----------------------------------------------------------------<br><BR>\n" );
document.write( "1 winning ticket worth $200; expected value to ticket holder $200-$1 = $199<BR>\n" );
document.write( "<s>2 winning tickets worth $100 each;</s> 1 winning ticket worth $100; expected value to ticket holder $100-$1 = $99<BR>\n" );
document.write( "4 winning tickets worth $20 each; expected value to ticket holders $20-1 = $19<BR>\n" );
document.write( "994 tickets worth nothing; expected value to ticket holders -$1<br><BR>\n" );
document.write( "Expected value for one ticket:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F1000%29%28199%29%2B%281%2F1000%29%2899%29%2B%284%2F1000%29%2819%29%2B%28994%2F1000%29%28-1%29+=+%28199%2B99%2B76-994%29%2F1000+=+%28374-994%29%2F1000+=+-620%2F1000+=+-0.62 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That was with a straightforward use of the formal definition of expected value.<br><BR>\n" );
document.write( "Here is an easier way to find the answer for this particular type of expected value problem:<br><BR>\n" );
document.write( "Total cost of the 1000 tickets at $1 each: $1000<br><BR>\n" );
document.write( "Total value of the prizes: $200 + $100 + 4*$20 = $380<br><BR>\n" );
document.write( "Expected value of one ticket: $380/1000 = $0.38<br><BR>\n" );
document.write( "\"Expected\" (actual) cost of ticket: $1.00<br><BR>\n" );
document.write( "Expected value of winning for 1 ticket: $0.38 - $1.00 = -$0.62<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );