document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186121>Question 1186121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tickets for a raffle cost $12. There were 713 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1800 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849478 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the expected value of a raffle ticket:\r<BR>\n" );
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document.write( "**1. Calculate the probability of winning:**\r<BR>\n" );
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document.write( "* There is 1 winning ticket out of 713 total tickets.<BR>\n" );
document.write( "* Probability of winning = 1/713\r<BR>\n" );
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document.write( "**2. Calculate the net winnings if you win:**\r<BR>\n" );
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document.write( "* You win $1800, and you get your $12 ticket cost back.<BR>\n" );
document.write( "* Net winnings = $1800 + $12 = $1812\r<BR>\n" );
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document.write( "**3. Calculate the net loss if you lose:**\r<BR>\n" );
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document.write( "* You lose the cost of the ticket.<BR>\n" );
document.write( "* Net loss = -$12\r<BR>\n" );
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document.write( "**4. Calculate the expected value:**\r<BR>\n" );
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document.write( "Expected Value = (Probability of Winning * Net Winnings) + (Probability of Losing * Net Loss)\r<BR>\n" );
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document.write( "Expected Value = (1/713 * $1812) + (712/713 * -$12)\r<BR>\n" );
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document.write( "Expected Value ≈ $2.54 + (-$11.96)\r<BR>\n" );
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document.write( "Expected Value ≈ -$9.42\r<BR>\n" );
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document.write( "**Therefore, the expected value of the raffle ticket is approximately -$9.42.** This means that on average, a person buying a ticket can expect to lose about $9.42.<BR>\n" );
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