document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209575>Question 1209575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lottery Prizes A lottery offers one $900 prize, two $700 prizes, two $400 prizes, and five $100 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person buys three tickets. 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 for currency problems. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849548 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I don't know what to make of the statement that \"the player's ticket is replaced after each draw and that the same ticket can win more than one prize\".  That seems unusual; and I'm not sure it changes how to calculate the expected value.<br><BR>\n" );
document.write( "I will leave it to another tutor to show a solution using the formal definition of expected value.  A less formal common sense solution is much easier.<br><BR>\n" );
document.write( "The total cost of the tickets is 1000*($5) = $5000.<br><BR>\n" );
document.write( "The total payout is $900 + 2*($700) + 2*($400) + 5*($100) = $3600.<br><BR>\n" );
document.write( "Overall, the \"gain\" is $3600 - $5000 = -$1400.<br><BR>\n" );
document.write( "The expected value for each of the 1000 tickets is (-$1400)/1000 = -$1.40.<br><BR>\n" );
document.write( "The expected value for 3 tickets is 3*(-$1.40) = -$4.20.<br><BR>\n" );
document.write( "ANSWER: -$4.20<br><BR>\n" );
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