document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176431>Question 1176431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 4 or a 6, nothing otherwise. What is your expected value? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803343 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=803343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor answered a different problem, using a pair of dice instead of a single die.<br><BR>\n" );
document.write( "Since the die is fair, the probabilities of each number coming up are the same.  So the expected value is the average gain or loss if the game is played 6 times and you get each number once.<br><BR>\n" );
document.write( "In doing that, you pay $18 ($3 for each of the 6 rolls) and you get $10 back.  You played the game 6 times and lost $8; your average gain/loss is (-18+10)/6 = -4/3.<br><BR>\n" );
document.write( "ANSWER: your expected value is -4/3, meaning on average you will lose about $1.33 each time you play.<br><BR>\n" );
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