document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197311>Question 1197311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. In a game,using a fair die, a player bet #5 on a given number shows up, otherwise the #5 bet is won. What is the expected value of the game.<BR>\n" );
document.write( "2. 5000 ticket is sold at #5 each for a raffle, ticket are to be drawn at random and price of #1000 each, 5 price of #200 each 20 price of #50 each. A man buy one of the raffle ticket. (a) what is the expected value for the man. <BR>\n" );
document.write( "(b) calculate the probability that he win a price. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848400 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Expected Value of the Die Game**\r<BR>\n" );
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document.write( "* **Probability of Winning:** 1/6 (since there's one desired number on a 6-sided die)<BR>\n" );
document.write( "* **Probability of Losing:** 5/6<BR>\n" );
document.write( "* **Payoff for Winning:** $0 (bet is lost)<BR>\n" );
document.write( "* **Payoff for Losing:** -$5 (bet amount)\r<BR>\n" );
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document.write( "* **Expected Value:** (Probability of Winning * Payoff for Winning) + (Probability of Losing * Payoff for Losing) <BR>\n" );
document.write( "    = (1/6) * $0 + (5/6) * (-$5) <BR>\n" );
document.write( "    = -$4.17\r<BR>\n" );
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document.write( "**Therefore, the expected value of the die game is -$4.17.** This means, on average, you're expected to lose $4.17 per game.\r<BR>\n" );
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document.write( "**2. Raffle Ticket Analysis**\r<BR>\n" );
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document.write( "* **Total Tickets Sold:** 5000<BR>\n" );
document.write( "* **Prizes:**<BR>\n" );
document.write( "    * 1 prize of $1000<BR>\n" );
document.write( "    * 5 prizes of $200<BR>\n" );
document.write( "    * 20 prizes of $50\r<BR>\n" );
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document.write( "* **Total Prizes:** 1 + 5 + 20 = 26\r<BR>\n" );
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document.write( "* **(a) Probability of Winning a Prize:** <BR>\n" );
document.write( "    * Number of Winning Tickets / Total Tickets <BR>\n" );
document.write( "    * = 26 / 5000 <BR>\n" );
document.write( "    * = 0.0052 <BR>\n" );
document.write( "    * = 0.52%\r<BR>\n" );
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document.write( "* **(b) Expected Value for the Man:**\r<BR>\n" );
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document.write( "    * **Total Prize Money:** <BR>\n" );
document.write( "        * ($1000 * 1) + ($200 * 5) + ($50 * 20) = $1000 + $1000 + $1000 = $3000\r<BR>\n" );
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document.write( "    * **Expected Winnings:** <BR>\n" );
document.write( "        * (Total Prize Money / Total Tickets) - Cost of Ticket <BR>\n" );
document.write( "        * = ($3000 / 5000) - $5 <BR>\n" );
document.write( "        * = $0.60 - $5 <BR>\n" );
document.write( "        * = -$4.40\r<BR>\n" );
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document.write( "**Therefore, the expected value for the man is -$4.40.** This means, on average, he can expect to lose $4.40 per raffle ticket.<BR>\n" );
document.write( " </SPAN>\n" );
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