document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039095>Question 1039095</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A raffle has a grand prize of a European cruise valued at $13000 with a second prize of a Las Vegas getaway valued at $1400. If each ticket costs $2 and 10600 tickets are sold, what are the expected winnings for a ticket buyer? Express to at least three decimal place accuracy in dollar form (as opposed to cents). <BR>\n" );
document.write( "Answer: $ \r<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 #653862 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=653862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first prize is 13000 and second prize is 1400.<BR>\n" );
document.write( "there are 10600 tickets sold.<BR>\n" );
document.write( "the probability of getting the grand prize is 1/10600.<BR>\n" );
document.write( "the probability of getting the second prize is also 1/10600.\r<BR>\n" );
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document.write( "you pay 2 dollars for the ticket.<BR>\n" );
document.write( "the probability of winning 13000 is 1/10600.<BR>\n" );
document.write( "the probability of winning 1400 is 1/10600.\r<BR>\n" );
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document.write( "your expected value is -2 + 1/10600 * 13000 + 1/10600 * 1400.<BR>\n" );
document.write( "that equates to expected value of -.641509434.<BR>\n" );
document.write( "round that to 3 decimal places and the expected winnings are -.642 dollars.\r<BR>\n" );
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document.write( "one way to look at this is as follows:\r<BR>\n" );
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document.write( "there are 10600 tickets sold at 2 dollars apiece.<BR>\n" );
document.write( "total money shelled out is 10600 * 2 = 21200.<BR>\n" );
document.write( "one ticket wins 13000.<BR>\n" );
document.write( "one ticket wins 1400.<BR>\n" );
document.write( "total value of all tickets sold is therefore -21200 + 13000 + 1400  = -6800<BR>\n" );
document.write( "the average gain on each ticket is therefore -6800 / 10600 = -.641509434.<BR>\n" );
document.write( "since a negative gains is a positive loss, then the average loss on each ticket is .641509434.<BR>\n" );
document.write( "since you were asked for expected winnings, you would report the expected gain which is negative, after you rounded it to 3 decimal places to get -.642. </SPAN>\n" );
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