document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026010>Question 1026010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A state lottery ticket costs $1. The probability of winning $1,000,000 is 0.0000001,  the probability of winning $1,000 is 0.000005, and the probability of winning $10 is 0.0002.  Find the expected value (gain or loss) on one ticket.\r<BR>\n" );
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document.write( "I have created my chart with outcomes, probabilty & x* pr but am having trouble getting the expected vaule , can you please assist? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641352 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the expected gain or loss, we proceed as follows:<BR>\n" );
document.write( "If you win $1,000,000, your gain is $999,999. (Because of the $1 you spent in buying the ticket.) This has probability 0.0000001.<BR>\n" );
document.write( "If you win $1,000, your gain is $999 (again because of similar reasoning as above).  This event has probability 0.000005.<BR>\n" );
document.write( "If you win $10, your gain is $9 (Should be easy now.)  This event has probability 0.0002.<BR>\n" );
document.write( "If you don't win at all, you gain -$1 (a loss!).  This event has probability 1 - 0.0000001 - 0.000005 - 0.0002 = 0.9997949.<BR>\n" );
document.write( "Thus the expected gain or loss is <BR>\n" );
document.write( "999,999*0.000001 + 999*0.000005 + 9*0.0002 + (-1)*0.9997949 = -$0.893.\r<BR>\n" );
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document.write( "Therefore expect to lose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2889+cents%29 ALIGN=MIDDLE  ALT=\"highlight%2889+cents%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > when you buy a lottery ticket!<BR>\n" );
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