document.write( "Question 1188314: If a person draws four cards from standard deck without replacing them, what is
\n" ); document.write( "the probability that at least one of the cards is face card ? \n" ); document.write( "
Algebra.Com's Answer #819364 by Edwin McCravy(20054)\"\" \"About 
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document.write( "There are 3 kinds of face cards, jacks, queens, and kings, and four suits of\r\n" );
document.write( "each which makes 3*4=12 face cards in a 52-card deck.  So there are 52-12=40\r\n" );
document.write( "non-face cards.\r\n" );
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document.write( "When you see the words \"at least one\", always first find the probability of the\r\n" );
document.write( "so-called complement event, the event of failing.  That is, we find the\r\n" );
document.write( "probability of completely failing to get any face cards at all and then subtract\r\n" );
document.write( "from 1 to get the probability of succeeding (getting at least one face card).\r\n" );
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document.write( "The number of ways he can fail, that is, to draw four cards from just the 40\r\n" );
document.write( "non-face-cards, is C(40,4) = 91390 ways.\r\n" );
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document.write( "The number of ways he can draw any four cards from the entire 52-card deck is\r\n" );
document.write( "C(52,4) = 270725 ways.\r\n" );
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document.write( "So the probability of failing to get a face card is to get one of the 91390 ways\r\n" );
document.write( "to fail out of the 270725 ways to get any four cards.\r\n" );
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document.write( "That's a probability of failing of 91390/270725 which reduces to 1406/4165,\r\n" );
document.write( "which is approximately the decimal 0.33757503.\r\n" );
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document.write( "So the probability of succeeding is that probability subtracted from 1 and\r\n" );
document.write( "1 -  1406/4165 is 2759/4165 which is about 0.66242497 or 66.2%. \r\n" );
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document.write( "Edwin
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