document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205333>Question 1205333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a raffle where 3500 tickets are sold for $2 each, one prize of $4800 will be awarded. What is the expected value of a single ticket in the raffle?<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 #842064 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=842064\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's say one single person buys all 3500 tickets.\r<BR>\n" );
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document.write( "They would spend 3500*2 = 7000 dollars in total.<BR>\n" );
document.write( "They would have 100% probability of getting the prize of $4800. <BR>\n" );
document.write( "But they walk away with a net loss of 4800 - 7000 = -2200 dollars.\r<BR>\n" );
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document.write( "Divide this net loss over the number of tickets.<BR>\n" );
document.write( "-2200/3500 = -0.62857 approximately<BR>\n" );
document.write( "This rounds to <font color=red>-0.63</font> which is the approximate expected value.\r<BR>\n" );
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document.write( "The person should expect to lose, on average, around 63 cents per ticket.\r<BR>\n" );
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document.write( "Another approach is to set up a table as shown below<BR>\n" );
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document.write( "<thead><tr><th>Event</th><th>X</th><th>P(X)</th><th>X*P(X)</th></tr></thead><tbody><tr><TD >Win</TD><TD >4798</TD><TD >1/3500</TD><TD >4798/3500</TD></tr><tr><TD >Lose</TD><TD >-2</TD><TD >3499/3500</TD><TD >-6998/3500</TD></tr></tbody>\n" );
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document.write( "where X = net earnings = amount you walk away with<BR>\n" );
document.write( "Note that 4800 - 2 = 4798<BR>\n" );
document.write( "P(X) = probability of getting those earnings\r<BR>\n" );
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document.write( "The X*P(X) column is the result of multiplying each X and P(X) value together. \r<BR>\n" );
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document.write( "Add up those X*P(X) values:<BR>\n" );
document.write( "4798/3500 + (-6998/3500)<BR>\n" );
document.write( "4798/3500 - 6998/3500<BR>\n" );
document.write( "(4798 - 6998)/3500<BR>\n" );
document.write( "-2200/3500<BR>\n" );
document.write( "-0.62857 approximately<BR>\n" );
document.write( "That leads to <font color=red>-0.63</font> when rounding to the nearest cent.\r<BR>\n" );
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document.write( "Answer: <font color=red>-0.63 dollars</font><BR>\n" );
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