document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=729303>Question 729303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two dice are rolled in a game you pay $1.00 to play. If a total lower than 5 comes up, you win $5.00, if a total greater than 9 comes up you win $2.00, otherwise you lose your dollar for playing. Calculate the expected value of playing,and the price of the game making it fair.\r<BR>\n" );
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document.write( "Good luck, I'm not einstein. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #445809 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=445809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two dice are rolled in a game you pay $1.00 to play.<BR>\n" );
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document.write( "If a total lower than 5 comes up, you win $5.00, <BR>\n" );
document.write( "ways to do that: 1/1,1/2,1/3,2/1,2/2,3/1 -----6 ways<BR>\n" );
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document.write( "if a total greater than 9 comes up you win $2.00,<BR>\n" );
document.write( "Ways to do that: <BR>\n" );
document.write( "4/6----------------------1<BR>\n" );
document.write( "5/5,5/6------------------2<BR>\n" );
document.write( "6/4,6/5,6/6--------------3<BR>\n" );
document.write( "Total-----------------------------------------6 ways<BR>\n" );
document.write( "otherwise you lose your dollar for playing. <BR>\n" );
document.write( "Total-----------------------------------------24 ways<BR>\n" );
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document.write( "Calculate the expected value of playing,<BR>\n" );
document.write( "Random Value:.....$4......$1......-1<BR>\n" );
document.write( "Probabilities.....1/6.....1/6.....4/6<BR>\n" );
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document.write( "Expected gain: (4 + 1 - 4)/6 = 1/6 or 16 2/3 cents<BR>\n" );
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document.write( "and the price of the game making it fair.<BR>\n" );
document.write( "You should pay $1.67 to play<BR>\n" );
document.write( "Then your expected winning would be zero and the game would be fair.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H <BR>\n" );
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