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 #849489 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52798)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Tickets for a raffle cost $12. There were 713 tickets sold. One ticket will be randomly selected <BR>\n" );
document.write( "as the winner, and that person wins $1800 and also the person is given back the cost of the ticket. <BR>\n" );
document.write( "For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?<BR>\n" );
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document.write( "I do not agree with the solution in the post by @CPhill.\r<BR>\n" );
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document.write( "    He calculates the net winning of the winner as\r\n" );
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document.write( "        Net winnings = $1800 + $12 = $1812.\r\n" );
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document.write( "    @CPhill adds $12 to the winning, but forgets to subtract $12 for buying the ticket.\r\n" );
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document.write( "    The correct way to calculate and the correct value of the net winning is, of course,\r\n" );
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document.write( "        - $12 + $1800 + $12 = $1800.\r\n" );
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document.write( "    Accordingly, all other numbers in the solution should be changed.\r\n" );
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document.write( "After that explanation, see my correct solution below.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>S O L U T I O N</U>\r<BR>\n" );
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document.write( "Here's how to calculate the expected value of a raffle ticket:\r\n" );
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document.write( "**1. Calculate the probability of winning:**\r\n" );
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document.write( "* There is 1 winning ticket out of 713 total tickets.\r\n" );
document.write( "* Probability of winning = 1/713\r\n" );
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document.write( "**2. Calculate the net winnings if you win:**\r\n" );
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document.write( "* You spent @12 to buy a ticket, win $1800, and you get your $12 ticket cost back.   <<<---=== my corrections start from this point\r\n" );
document.write( "* Net winnings = - $12 + $1800 + $12 = $1800\r\n" );
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document.write( "**3. Calculate the net loss if you lose:**\r\n" );
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document.write( "* You lose the cost of the ticket.\r\n" );
document.write( "* Net loss = -$12\r\n" );
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document.write( "**4. Calculate the expected value:**\r\n" );
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document.write( "Expected Value = (Probability of Winning * Net Winnings) + (Probability of Losing * Net Loss)\r\n" );
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document.write( "Expected Value = (1/713 * $1800) + (712/713 * (-$12))\r\n" );
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document.write( "Expected Value ≈ -$-9.458625526     <<<---===  notice the difference with the value by -$9.42 in the solution by @CPhill\r\n" );
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document.write( "                                    <<<---===  also notice that I do not round it to cents, since this value is the statistical quantity\r\n" );
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document.write( "**Therefore, the expected value of the raffle ticket is approximately -$9.46.** This means that on average, a person buying a ticket can expect to lose about $9.46.\r\n" );
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document.write( "Solved correctly.\r<BR>\n" );
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document.write( "The difference may seem not to be significant, but in this problem not the magnitude of the difference<BR>\n" );
document.write( "plays a role, but the correctness of the approach, developing right logic and the correctness of steps.\r<BR>\n" );
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document.write( "For the solution by @CPhill, strict examiner would give a solid &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%282%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;and would send him for retraining.\r<BR>\n" );
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