document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981077>Question 981077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a carnival game you pay $3 for a ticket to spin the wheel and win the amount shown. The odds are listed below:\r<BR>\n" );
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document.write( "25% chance win $0 <BR>\n" );
document.write( "25% chance win $2 <BR>\n" );
document.write( "50% chance win $5 <BR>\n" );
document.write( "1.Calculate the expected value for this game according to these directions:\r<BR>\n" );
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document.write( "a).Multiply the probability of the event occurring times the payoff for that event.<BR>\n" );
document.write( "b).Repeat step 1 for all possible events<BR>\n" );
document.write( "c).Sum up all the results from steps 1 and 2\r<BR>\n" );
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document.write( "2.Is this a fair game? (Does the amount you pay = what you expect to win)\r<BR>\n" );
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document.write( "I am completely lost on this one. Any help is greatly appreciated!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602101 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=602101\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)\r<BR>\n" );
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document.write( "Factoring in the cost to play the game ($3)\r<BR>\n" );
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document.write( "If you win $0, then you really gain -3 dollars (ie you lost $3)<BR>\n" );
document.write( "If you win $2, then you really gain -1 dollars (ie you lost $1)<BR>\n" );
document.write( "If you win $5, then you really gain 2 dollars (you finally have won some money)\r<BR>\n" );
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document.write( "<tr><th>Probability</th><th>Net Gain</th></tr><tr><TD >0.25</TD><TD >-3</TD></tr><tr><TD >0.25</TD><TD >-1</TD></tr><tr><TD >0.50</TD><TD >2</TD></tr>\n" );
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document.write( "Multiply the probabilities with their corresponding net gain\r<BR>\n" );
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document.write( "0.25*(-3) = -0.75<BR>\n" );
document.write( "0.25*(-1) = -0.25<BR>\n" );
document.write( "0.50*(2) = 1\r<BR>\n" );
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document.write( "Add up those results\r<BR>\n" );
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document.write( "-0.75+(-0.25)+1 = 0\r<BR>\n" );
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document.write( "The expected value is 0.\r<BR>\n" );
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document.write( "2)\r<BR>\n" );
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document.write( "From problem 1 above, we found the expected value to be 0. This is a fair game because, over the long run, you gain on average $0. You neither win money nor lose money. The same applies to the person running the game. Both sides (you and the person running the game) are equal.<BR>\n" );
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