document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117249>Question 1117249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is the old Monopoly question but I think the question is ambiguous.\r<BR>\n" );
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document.write( "In the game of Monopoly, a player who is in jail can get out of jail by throwing a double on the two dice on any of his or her next 3 turns. Both dice show 1, 2, 3, 4, 5, and 6. What is the probability that a player will get out of jail by throwing a double on the next 3 turns?\r<BR>\n" );
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document.write( "I interpreted \"by throwing a double on the next 3 turns\" as being a double on any of the next 3 turns as you only need to throw one double to get out of jail. But, my friend interpreted as being throwing a double on all three turns. \r<BR>\n" );
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document.write( "So, for me, I figured it would be 1/6 * 1/6 * 1/6 = 0.0046\r<BR>\n" );
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document.write( "My friend though is arguing it should be 1/6 + 1/6 + 1/6 = 0.5\r<BR>\n" );
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document.write( "Right now, we are both chasing our alegrabraic tales and just confusing each other. Thanks so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732254 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=732254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The problem is worded poorly, making different interpretations possible.  However, since the question is<br><BR>\n" );
document.write( "\"What is the probability that a player WILL GET OUT OF JAIL by throwing a double on the next 3 turns?\"<br><BR>\n" );
document.write( "I would agree with you that it is only asking the probability that the player will get out of jail by throwing a double on ONE of the next three turns.<br><BR>\n" );
document.write( "However, neither calculation you show is correct for the respective interpretations.<br><BR>\n" );
document.write( "For your friend's interpretation, that the player gets doubles on all three of the next turns, the probability is the calculation you show for YOUR interpretation: (1/6)*(1/6)*(1/6) = 1/216.<br><BR>\n" );
document.write( "For your interpretation, the probability has to interpreted as<BR>\n" );
document.write( "(1) get a double on turn 1, OR<BR>\n" );
document.write( "(2) not get a double on turn 1 AND get a double on turn 2, OR<BR>\n" );
document.write( "(3) not get a double on turn 1 AND not get a double on turn 2 AND get a double on turn 3<br><BR>\n" );
document.write( "Replacing the ORs with addition and the ANDs with multiplication, the calculation for that probability is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29%2B%285%2F6%29%281%2F6%29%2B%285%2F6%29%285%2F6%29%281%2F6%29+=+%281%2F6%29%2B%285%2F36%29%2B%2825%2F216%29+=+%2836%2B30%2B25%29%2F216+=+91%2F216 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Notice the probability can also be calculated as 1 minus the probability that he does NOT get a double on any of the next three turns:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+%285%2F6%29%285%2F6%29%285%2F6%29+=+1+-+125%2F216+=+91%2F216 ALIGN=MIDDLE  ALT=\"1+-+%285%2F6%29%285%2F6%29%285%2F6%29+=+1+-+125%2F216+=+91%2F216\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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