document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135683>Question 135683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would like to know what the probability of taking three cards from a full deck of cards and having at least one jack,queen or king in the three cards. I have been told that the answer is 12/52 X 12/51 X 12/50 or about 70% and I feel that this is wrong. Please advise how to figure this out. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99427 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=99427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the successful outcome is AT LEAST 1 face card in the 3 cards, you are faced with calculating the probability that there are exactly 3 face cards, then the probability that there are exactly 2, and then the probability that there is exactly 1, and then summing the result.  This is a very convoluted and complex calculation.\r<BR>\n" );
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document.write( "Much easier is to realize that if you draw 3 cards the probability that at least one is a face card plus the probability that NONE of them are face cards is certainty -- there are no other possibilities.  So, calculate the probability that NONE of them are face cards -- a fairly straightforward calculation -- and then subtract that value from 1.\r<BR>\n" );
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document.write( "In a standard deck of 52 cards, 3 times 4 = 12 of them are face cards and the other 40 are not face cards.\r<BR>\n" );
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document.write( "If I pick one card out of the deck, I have a 40/52 probability that it is not a face card.  Presuming I am successful and draw a non-face on the first draw, I will now have a deck with 51 total cards and 39 non-face, so my probability of drawing a second card that is non-face given that the first card was non-face is 39/51.  And the probability for the third card being non-face given that the first two were non-face is 38/50.\r<BR>\n" );
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document.write( "The total probability is then the product of these three probabilities:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840%2F52%29%2839%2F51%29%2838%2F50%29=59280%2F132600=.45 ALIGN=MIDDLE  ALT=\"%2840%2F52%29%2839%2F51%29%2838%2F50%29=59280%2F132600=.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to the nearest 0.01)\r<BR>\n" );
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document.write( "So the probability that you will draw at least 1 face card in a three card draw is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.45=0.55 ALIGN=MIDDLE  ALT=\"1-0.45=0.55\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Give me the name of this guy who told you it was 70%.  I want to play poker with him. </SPAN>\n" );
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