document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86634>Question 86634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Any help would be greatly appreciated.....\r<BR>\n" );
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document.write( "The following puzzler was given on the Car Talk radio program on February 19, 2001.* “Three different numbers are chosen at random, and one is written on each of three slips of paper. The slips are then placed face down on the table. The objective is to choose the slip upon which is written the largest number. Here are the rules: You can turn over any slip of paper and look at the amount written on it. If for any reason you think this is the largest, you’re done; you keep it. Otherwise you discard it and turn over a second slip. Again, if you think this is the one with the biggest number, you keep that one and the game is over. If you don’t, you discard that one too. . . . The chance of getting the highest number is one in three. Or is it? Is there a strategy by which you can improve the odds?”<BR>\n" );
document.write( "The answer to the puzzler is that you can indeed improve the probability of getting the highest number by the following strategy. Pick one of the slips of paper, and after looking at the number, throw it away. Then pick a second slip; if it has a larger number than the first slip, stop. If not, pick the third slip. Find the probability of winning with this strategy.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62672 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=62672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L represent the largest number<BR>\n" );
document.write( "Let M represent the middle number and<BR>\n" );
document.write( "Let S represent the smallest number<BR>\n" );
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document.write( "If you were to roll over the numbers one at a time until all three numbers show, there are<BR>\n" );
document.write( "six possible outcomes:<BR>\n" );
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document.write( "L then S then M<BR>\n" );
document.write( "L then M then S<BR>\n" );
document.write( "M then S then L<BR>\n" );
document.write( "M then L then S<BR>\n" );
document.write( "S then M then L<BR>\n" );
document.write( "S then L then M<BR>\n" );
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document.write( "Since all of these are equally likely, they each have a probability of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Notice that two of the outcomes have L as the first draw.  That means that the possibility<BR>\n" );
document.write( "of L being the first number you turn up is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6+%2B+1%2F6+=+2%2F6+=+1%2F3 ALIGN=MIDDLE  ALT=\"1%2F6+%2B+1%2F6+=+2%2F6+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "However, your system says that you ignore the first number and proceed. This means that<BR>\n" );
document.write( "at this point you have a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > chance of being wrong and losing.<BR>\n" );
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document.write( "Next look at the possibility that you draw M then S then L. By the rules of your \"system\" you<BR>\n" );
document.write( "discard the M, then draw the S, which being smaller than M, you also discard, and you end <BR>\n" );
document.write( "up drawing L on your last turnover. You win. There is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > chance of this happening.<BR>\n" );
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document.write( "Next possibility. You draw M then L and then S.  By your system you draw M, discard it,<BR>\n" );
document.write( "then draw L, and you quit without turning over the third number. You win!. There is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "chance of this outcome.<BR>\n" );
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document.write( "Next possibility. You draw S then M then L. By your system you draw S, discard it, then<BR>\n" );
document.write( "draw the M. This being larger than S, you quit ... and you lose because L has not been<BR>\n" );
document.write( "drawn.<BR>\n" );
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document.write( "Final possibility. You draw S then L then M. Again by your system, you draw S, discard it,<BR>\n" );
document.write( "then draw L. The L being larger than S tells you to quit. You do, and you win! There is<BR>\n" );
document.write( "a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > chance of this happening.<BR>\n" );
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document.write( "Adding it up, you see that you have 3 winning chances [MSL, MLS, SLM] each with a probability<BR>\n" );
document.write( "of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a total winning probability of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6+%2B+1%2F6+%2B+1%2F6+=+3%2F6+=+1%2F2 ALIGN=MIDDLE  ALT=\"1%2F6+%2B+1%2F6+%2B+1%2F6+=+3%2F6+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Your losing chances consist of the two chances that L is the first draw and the chance that<BR>\n" );
document.write( "the draw sequence would be SML and you stop at M.  This means that the total losing<BR>\n" );
document.write( "possibility is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6+%2B+1%2F6+%2B+1%2F6+=+3%2F6+=+1%2F2 ALIGN=MIDDLE  ALT=\"1%2F6+%2B+1%2F6+%2B+1%2F6+=+3%2F6+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So your winning chance using the system is fifty-fifty, a significant improvement <BR>\n" );
document.write( "over drawing the first number and quitting.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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