document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173901>Question 1173901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A lottery system has balls numbered 1 to 60 and randomly selects 7 of the lottery balls. There is only one prize of $5,600,000.00 which is awarded only if a lottery player selects the correct set of 7 lottery balls.\r<BR>\n" );
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document.write( "    a) If a lottery ticket costs $1.00, what is a lottery player's expected value? <BR>\n" );
document.write( "    b) How much would the lottery prize have to be worth if it was to be a fair game? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799222 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of combinations of 7 numbers is N = 60*59*58*57*56*55*54/7! = 386206920<BR>\n" );
document.write( "P(winning) = 1/N. Hence the probability of NOT winning = (N-1)/N<BR>\n" );
document.write( "The prize amount is $5.6M, and the ticket cost is $1.<BR>\n" );
document.write( "The expected value is therefore P(winning)*prize - P(losing)*ticket cost =<BR>\n" );
document.write( "(1/N)*$5.6M - ((N-1)/N)*$1 = -0.9855 ~-98.6. <BR>\n" );
document.write( "So you will lose almost 99 cents for every dollar bet.<BR>\n" );
document.write( "For a fair game, i.e. break even, P/N = (1 - 1/N) -> P = N - 1 = 386206919 = $386.2M </SPAN>\n" );
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