document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197615>Question 1197615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain raffle has one ticket that wins a $150 prize and five tickets that each win a $10 prize out of 150 purchased tickets.\r<BR>\n" );
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document.write( "Round answers to the nearest cent.\r<BR>\n" );
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document.write( "a. Find the expected value of each ticket. \r<BR>\n" );
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document.write( "b. For the company running the raffle, would selling each ticket for $5 be a Profit, a Loss, or a Fair Game?  </SPAN>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "Answer: <font color=red>$1.33</font>\r<BR>\n" );
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document.write( "Work Shown:<BR>\n" );
document.write( "X = winnings<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >P(X)</TD><TD >X*P(X)</TD></tr><tr><TD >150</TD><TD >1/150</TD><TD >1</TD></tr><tr><TD >10</TD><TD >5/150</TD><TD >1/3</TD></tr><tr><TD >0</TD><TD >144/150</TD><TD >0</TD></tr>\n" );
document.write( "</TABLE>Add up the results in the X*P(X) column<BR>\n" );
document.write( "E[X] = 1+1/3+0 = 4/3 = 1.33 approximately<BR>\n" );
document.write( "The expected winnings is $1.33 approximately.<BR>\n" );
document.write( "The player expects to win on average $1.33 per ticket (this is before the cost of the ticket is factored in).\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Answer: <font color=red>Profit</font>\r<BR>\n" );
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document.write( "Reason: <BR>\n" );
document.write( "The company expects to lose $1.33 per game when paying out the average winnings per ticket, as we found in part (a).<BR>\n" );
document.write( "However, they gain $5 per ticket if they go for this ticket price.<BR>\n" );
document.write( "The net profit per ticket from the company's perspective is -1.33+5 = 3.67<BR>\n" );
document.write( "The company expects to gain $3.67 per ticket; while player expects to lose $3.67 per ticket.<BR>\n" );
document.write( "These values represent averages.\r<BR>\n" );
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document.write( "If the ticket price was $1.33, then both sides neither win nor lose money. In such an event, we consider it a fair game. <BR>\n" );
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