document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099170>Question 1099170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you play a game of chance in which you toss a coin 3 times. You pay a nor refundable $2 to play the game. You win $10 in case your coin lands with a tail on top during the three tosses. You win nothing otherwise.\r<BR>\n" );
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document.write( " a)	Fill out the following probability distribution table.<BR>\n" );
document.write( "b)	Over the long term, what is your expected value of playing the game?<BR>\n" );
document.write( "c) If you played this game 100 times, how much would you expect win/loose? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713647 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=713647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>What does \"lands with a tail on top during the three tosses\" mean?<br><BR>\n" );
document.write( "It sounds as if it means tails at least once on the three tosses.  If that is the case, I want to know where I can play this game, because I'm going to win 7 out of 8 times.  The only way not to win is to get heads on all three tosses; the probability of that is (1/2)(1/2)(1/2) = 1/8; so the probability of winning is 7/8.<br><BR>\n" );
document.write( "If that is indeed the rule, then when you play the game 8 times you pay $2 each time (-$16); you win 7 times (+$70), and you lose 1 time (no change).  So for each 8 games your expected net would be +$54.  So the expected value of each game is $54/8 = $6.75.<br><BR>\n" );
document.write( "I don't think it is likely that that is the way the problem is supposed to go.  I suspect the rule is you win if you get tails on ALL THREE tosses.  Then the probability of winning is 1/8 and the probability of losing is 7/8.<br><BR>\n" );
document.write( "Then for 8 games you would again be paying $16, but you would only be winning $10 once.  So you would lose $6 every 8 games; that means the expected value for each game would be -$6/8 = -$0.75. </SPAN>\n" );
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