document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082068>Question 1082068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a standard deck of 52 cards<BR>\n" );
document.write( "(i) If you draw two cards from the deck without returning them. What is the probability that at<BR>\n" );
document.write( "least one will be a King?<BR>\n" );
document.write( "(ii) Four Queens are removed from the deck and placed face down on the table. If you turn over two of these cards, what is the probability that one is a red Queen and the other is a black Queen?<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 #696143 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=696143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (i)  P(Drawing two cards and having at least one be a king) is the same as 1 - P(no king appears in the draw)<BR>\n" );
document.write( "and the latter is easier to calculate directly:<BR>\n" );
document.write( "                              P (no king in a draw of 2 cards) = (48/52)*(47/51) = 564/663<BR>\n" );
document.write( "P(rawing two cards and having at least one be a king) =<BR>\n" );
document.write( "                1 - 564/663 = 99/663 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2833%2F221%29+ ALIGN=MIDDLE  ALT=\"highlight%2833%2F221%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or about 0.14932\r<BR>\n" );
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document.write( "(ii)  Say you pick the two cards one at a time from the 4 queens:  P(red then black) + P(black then red) =<BR>\n" );
document.write( "(2/4)*(2/3) + (2/4)*(2/3) = 8/12 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%282%2F3%29+ ALIGN=MIDDLE  ALT=\"+highlight%282%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "—<BR>\n" );
document.write( "This can be also be seen by the number of arrangements possible for the 4 queens:<BR>\n" );
document.write( "       RRBB, RBRB, RBBR, BBRR, BRBR, BRRB  and say you just deal out the first two of these, exactly<BR>\n" );
document.write( "4 out of the 6 possible arrangements will give you one R and one B.  <BR>\n" );
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