document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162300>Question 1162300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company is selling raffle tickets for $4. The first prize is $3500,<BR>\n" );
document.write( "and the second prize is $500. The company manages to sell 5000 tickets.<BR>\n" );
document.write( "X 3496 496 -4<BR>\n" );
document.write( "P(x) 1/5000 1/5000 4998/5000 \r<BR>\n" );
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document.write( "What is the Expected Value?<BR>\n" );
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document.write( "Formally, the expected value is the sum of each outcome multiplied by its probability.  So in this example the expected value is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5000%29%2A%283496%29%2B%281%2F5000%29%2A%28496%29%2B%284998%2F5000%29%2A%28-4%29+=+%283496%2B496-19992%29%2F5000+=+%28-16000%29%2F5000+=+-3.2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The expected value is -$3.20.<br><BR>\n" );
document.write( "While that is the formal mathematical way to calculate expected value, in many simple expected value problems like this, there is a much easier way to find the expected value.<br><BR>\n" );
document.write( "In this example, the total cost of the tickets is $20,000; the total payout is $3500+$500 = $4000.  The expected value is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284000-20000%29%2F5000+=+-16000%2F5000+=+-3.2 ALIGN=MIDDLE  ALT=\"%284000-20000%29%2F5000+=+-16000%2F5000+=+-3.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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