document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=381488>Question 381488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you have a set of three four sided dice. Your friend wants to bet that he/she can roll the number combination 1,2,3 (any combination i.e. no die shows a four, and no die duplicates another). She/he wants to roll the dice one hundred times and each time the combination 1,2,3 comes up you will give him/her one dollar, each time it does not come up she/he will give you 10 cents. How much would you expect to win or lose based on statistically theory.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270577 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=270577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose you have a set of three four sided dice. Your friend wants to bet that he/she can roll the number combination 1,2,3 (any combination i.e. no die shows a four, and no die duplicates another). She/he wants to roll the dice one hundred times and each time the combination 1,2,3 comes up you will give him/her one dollar, each time it does not come up she/he will give you 10 cents. How much would you expect to win or lose based on statistically theory. <BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "# of ways to get 1,2,3: 3*2*1 = 6<BR>\n" );
document.write( "# of possible outcomes: 6^3 = 216<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "P(getting 1,2,3) = 6/216 = 3/108 = 1/36<BR>\n" );
document.write( "============================================<BR>\n" );
document.write( "Expected winnings for me = (-10)(1/36) + (0.10)(35/36) <BR>\n" );
document.write( "= [-10+3.5]/36<BR>\n" );
document.write( "= -0.18<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "I can expect to lose 18 cents each time the dice are thrown.<BR>\n" );
document.write( "I can expect to lose $18 in 100 throws of the dice.<BR>\n" );
document.write( "================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );