document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119617>Question 1119617</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes. \r<BR>\n" );
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document.write( "One thousand tickets are sold at $6.00 each.  \r<BR>\n" );
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document.write( "Find the expectation if a person buys four tickets. \r<BR>\n" );
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document.write( "Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places. question 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735232 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=735232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> one prize worth 1000 dollars.<BR>\n" );
document.write( "two prizes worth 700 dollars each.<BR>\n" );
document.write( "three prizes worth 300 dollars each.<BR>\n" );
document.write( "four prizes worth 200 dollars each.\r<BR>\n" );
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document.write( "one thousand tickets sold at 6 dollars each.\r<BR>\n" );
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document.write( "probability of winning 1000 dollars on a ticket is equal to 1/1000.<BR>\n" );
document.write( "probability of winning 700 dollars on a ticket is equal to 2/1000.<BR>\n" );
document.write( "probability of winning 300 dollars on a ticket is equal to 3/1000.<BR>\n" );
document.write( "probability of winning 200 dollars on a ticket is equal to 4/1000.\r<BR>\n" );
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document.write( "the expectation for that one ticket is therefore:\r<BR>\n" );
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document.write( "1/1000 * 1000 + 2/1000 * 700 + 3/1000 * 300 + 4/1000 * 200 - 6.\r<BR>\n" );
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document.write( "that is equal to -1.9 dollars.\r<BR>\n" );
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document.write( "since the tickets can be reused, then each time the probability remains the same.\r<BR>\n" );
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document.write( "his total probability is therefore 4 * -1.9 = -7.6 dollars.\r<BR>\n" );
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document.write( "suppose that, for some reason, he bought all 1000 tickets.\r<BR>\n" );
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document.write( "he's guaranteed to win all the prizes but he has to pay for all the tickets.\r<BR>\n" );
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document.write( "he will gain 1000 + 2 * 700 + 3 * 300 + 4 * 100 = 4100, but he will lose <BR>\n" );
document.write( "1000 * 6 = 6000 dollars.\r<BR>\n" );
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document.write( "his expectation is therefore 4100 - 6000 = -1900.\r<BR>\n" );
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document.write( "divide that by the 1000 tickets and the loss averages out to 1.9 dollars on each ticket.\r<BR>\n" );
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document.write( "that would be his expectation on each ticket that he buys.\r<BR>\n" );
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document.write( "he buys 4.\r<BR>\n" );
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document.write( "4 * an average lose of 1.9 on each ticket means a total average loss of 7.6 dollars.\r<BR>\n" );
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document.write( "if the tickets are not replaced on each draw, then the probabilities on each draw change.\r<BR>\n" );
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document.write( "since they are replaced, the probabilities remain the same on each draw.\r<BR>\n" );
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document.write( "i believe that's your answer.\r<BR>\n" );
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document.write( "hopefully it's correct.\r<BR>\n" );
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document.write( "if not, then let me know what the correct answer should be, since i haven't seen a problem like this one before.\r<BR>\n" );
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document.write( "usually it's the expectation on one draw.\r<BR>\n" );
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document.write( "replacing the ticket does keep the expectation on each draw the same, which is why i'm assuming the expectation is 4 * the expectatikon on 1 draw.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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