document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200362>Question 1200362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tickets for a raffle cost $15. There were 758 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1300. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?\r<BR>\n" );
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document.write( "If the Expected Value is negative, be sure to include the \"-\" sign with the answer. Express the answer rounded to two decimal places.\r<BR>\n" );
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document.write( "Expected Value = $ \r<BR>\n" );
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document.write( "(PLEASE EXPLAIN) I do not understand, and it would be a lot if the steps were shown. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834475 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer = <font color=red size=4>-13.28</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "X = net winnings\r<BR>\n" );
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document.write( "If a person wins $1300, and the ticket costs $15, then they walk away with $1285 (since 1300-15 = 1285)<BR>\n" );
document.write( "In short: X = 1285 is one possibility.\r<BR>\n" );
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document.write( "The other outcome is when X = -15 to represent cases when the person doesn't win anything. Even worse: They lost $15.\r<BR>\n" );
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document.write( "There's 1 winning ticket out of 758 total<BR>\n" );
document.write( "1/758 represents the probability of winning, so it's tied to X = 1285<BR>\n" );
document.write( "In other words, P(X) = 1/758 when X = 1285\r<BR>\n" );
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document.write( "1-(1/758) = 757/758 is the probability connected to X = -15\r<BR>\n" );
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document.write( "To summarize so far<ul><li>P(X) = 1/758 when X = 1285</li><li>P(X) = 757/758 when X = -15</li></ul>Often it's handy to organize this information into a table <BR>\n" );
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document.write( "<tr><TD >X</TD><TD >P(X)</TD></tr><tr><TD >1285</TD><TD >1/758</TD></tr><tr><TD >-15</TD><TD >757/758</TD></tr>\n" );
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document.write( "Use of spreadsheet software is strongly recommended. \r<BR>\n" );
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document.write( "We'll then form a new column labeled X*P(X)<BR>\n" );
document.write( "This is where we multiply each X with its corresponding P(X) value<BR>\n" );
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document.write( "<tr><TD >X</TD><TD >P(X)</TD><TD >X*P(X)</TD></tr><tr><TD >1285</TD><TD >1/758</TD><TD >1285/758</TD></tr><tr><TD >-15</TD><TD >757/758</TD><TD >-11355/758</TD></tr>\n" );
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document.write( "Then we add up the results of that new column.<BR>\n" );
document.write( "(1285/758)+(-11355/758)<BR>\n" );
document.write( "(1285-11355)/758<BR>\n" );
document.write( "-10070/758<BR>\n" );
document.write( "-13.2849604221636<BR>\n" );
document.write( "<font color=red>-13.28</font>\r<BR>\n" );
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document.write( "That is the approximate expected value. More specifically, it's the approximate expected net winnings.<BR>\n" );
document.write( "It means that the average person expects to lose about $13.28\r<BR>\n" );
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document.write( "-----------------------------------------\r<BR>\n" );
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document.write( "Another approach:\r<BR>\n" );
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document.write( "The previous method used the standard textbook approach with expected value problems. That template outline being: <ol><li>Construct the probability distribution table of each X and P(X)</li><li>Compute X*P(X) for each row.</li><li>Add up each X*P(X) value</li></ol>For this second approach, imagine a single person buying all 758 tickets at $15 each.<BR>\n" );
document.write( "In total, they spent 758*15 = 11370 dollars.\r<BR>\n" );
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document.write( "That means they are down this amount. <BR>\n" );
document.write( "We write -11370 to indicate this loss.\r<BR>\n" );
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document.write( "But this player is guaranteed to win the prize of $1300 because they bought all the tickets.<BR>\n" );
document.write( "Their net winnings is -11370+1300 = -10070<BR>\n" );
document.write( "They're still down a considerable amount of money.\r<BR>\n" );
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document.write( "Divide this net loss over the number of tickets to determine the average loss per ticket.<BR>\n" );
document.write( "-10070/758 = -13.2849604221636 = <font color=red>-13.28</font>\r<BR>\n" );
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document.write( "Therefore, this player lost on average approximately $13.28 per ticket.\r<BR>\n" );
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document.write( "Hopefully you notice that these calculations are very similar to the previous section's calculations. <BR>\n" );
document.write( "The numbers haven't changed too much. <BR>\n" );
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