document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472758>Question 472758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8. One thousand raffle tickets are sold for $1.00 each. One grand prize of $200 and two consolation prizes of $50 each will be awarded. Jeremy purchases one ticket. Find his expected value. Show your work for full credit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324103 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=324103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1000 raffle tickets are sold.<BR>\n" );
document.write( "997 return nothing.<BR>\n" );
document.write( "2 return 50 each.<BR>\n" );
document.write( "1 returns 200.<BR>\n" );
document.write( "probability of getting nothing back is 997/1000 = .997<BR>\n" );
document.write( "probability of getting 50 back is 2/1000 = .002<BR>\n" );
document.write( "probability of getting 200 back is 1/1000 = .001<BR>\n" );
document.write( "he expects to get back:<BR>\n" );
document.write( ".997 * 0 + .002 * 50 + .001 * 200 = .3 = 30 cents.<BR>\n" );
document.write( "since he paid 1.00 for the ticket, then his total expected value is -.7.<BR>\n" );
document.write( "this means that he will lose 70 cents per ticket on the average.<BR>\n" );
document.write( "assume he bought all 1000 tickets.<BR>\n" );
document.write( "he would be out 1000 dollars.<BR>\n" );
document.write( "he would get nothing back on 997 of them.<BR>\n" );
document.write( "he would get 50 back on 2 of them for 100 dollars.<BR>\n" );
document.write( "he would get 200 back on 1 of them for 100 dollars.<BR>\n" );
document.write( "his net value for the 1000 tickets would be - 700.<BR>\n" );
document.write( "divide that by 1000 to get an average of -.7 per ticket.<BR>\n" );
document.write( "you could have also looked at it as follows:<BR>\n" );
document.write( ".997 of the time he would be - 1.00 (buys ticket and gets nothing back).<BR>\n" );
document.write( ".002 of the time he would be + 49 (gets back 50 but loses 1).<BR>\n" );
document.write( ".001 of the time he would be + 199 (gets back 200 but loses 1).<BR>\n" );
document.write( "total expected value would be:<BR>\n" );
document.write( ".997 * (-1) + .002 * (49) + .001 * (199) = -.7\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );