document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129581>Question 1129581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5.	Raffle Tickets Ten thousand raffle tickets are sold for $5 each. Four prizes will be awarded: one for $5000, one for $2500, and two for $1000. Assume that the probability that any given ticket is selected for the $5000 prize is 110,000110,000, the probability that any given ticket is selected for the $2500 prize is 110,000110,000, and the probability that any given ticket is selected for a $1000 prize is 210,000210,000.<BR>\n" );
document.write( "Sidhardt purchases one of these tickets.<BR>\n" );
document.write( "a.	Determine his expected value.<BR>\n" );
document.write( "b.	Determine the fair price of a ticket.<BR>\n" );
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document.write( "a. expected value for one ticket<br><BR>\n" );
document.write( "The expected winnings on one ticket are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F10000%29%2A5000%2B%281%2F10000%29%2A2500%2B%282%2F10000%29%2A1000%2B%289996%2F10000%29%2A0+=+9500%2F10000+=+0.95 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The cost of the ticket is $5; the expected winnings are $0.95.  The expected value of the ticket is -$4.05.<br><BR>\n" );
document.write( "b. fair price of a ticket<br><BR>\n" );
document.write( "The ticket price is fair (the raffle makes no money) if the cost of the tickets is equal to the total amount of the prizes.<br><BR>\n" );
document.write( "The total amount of the prizes is $9500; the number of tickets is 10,000.  A fair price for a ticket is $9500/10000 = $0.95.<br><BR>\n" );
document.write( "Alternatively, the ticket price is fair if the cost of the ticket is equal to the expected winnings.  Since the expected winnings for one ticket is $0.95, that is the fair price of a ticket. </SPAN>\n" );
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