document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=235056>Question 235056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> five cards are dealt, what is the probability that the fifth one is a king </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173246 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=173246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Depends on whether you can see the value of the first four or not.\r<BR>\n" );
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document.write( "If you don't know the value of the first four cards, then there are 4 kings in 52 cards, or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P_{K}\ =\ \frac{1}{13}\">.\r<BR>\n" );
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document.write( "On the other hand, if you can see the first four cards, then the denominator of the fraction changes from 52 to 48, that is 52 minus the 4 cards you can see leaving you 48 cards you don't know about.  The numerator is a little more complicated.\r<BR>\n" );
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document.write( "The numerator of the probability depends on the number of kings that appear in the first 4 cards.  Quite obviously, if the first 4 cards are themselves kings, then the probability that the fifth card will be a king is zero -- because there aren't any left.\r<BR>\n" );
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document.write( "So, let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> represent the number of kings that appear in the first four cards, then the probability that the fifth card is a king is calculated by the following:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_K\ = \frac{4\ -\ n}{48}\">,\r<BR>\n" );
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document.write( "and you can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 0\ \leq\ P_K\ \leq\ \frac{1}{12}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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