document.write( "Question 1142552: Three cards are dealt from a standard deck of fifty-two cards (without replacement); the probability that there is at least one face card? \n" ); document.write( "

Algebra.Com's Answer #763251 by Edwin McCravy(20065) $\"\"$ $\"About$

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Three cards are dealt from a standard deck of fifty-two cards (without replacement); the probability that there is at least one face card?
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document.write( "The entire deck of cards are these 52:\r\n" );
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document.write( "A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ \r\n" );
document.write( "A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦\r\n" );
document.write( "A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  \r\n" );
document.write( "A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣ \r\n" );
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document.write( "The number of ways to select ANY three cards from those 52 is\r\n" );
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document.write( "52 cards choose 3 = 52C3 = 22100 ways.  That will be the denominator\r\n" );
document.write( "of our probability before reducing.\r\n" );
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document.write( "But for the complement event, we remove the face cards, which leaves\r\n" );
document.write( "these cards\r\n" );
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document.write( "A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥ \r\n" );
document.write( "A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦\r\n" );
document.write( "A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  \r\n" );
document.write( "A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣\r\n" );
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document.write( "So the numer of ways to select three cards from those 40 is\r\n" );
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document.write( "40 cards choose 3 = 40C3 = 9880\r\n" );
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document.write( "So the probability of the complement event is\r\n" );
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document.write( "9880 ways out of 22100 or  which reduces to\r\n" );
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document.write( "  <-- probability of complement event of dealing\r\n" );
document.write( "NO face cards,\r\n" );
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document.write( "Therefore the probabilkity of selecting at least one face\r\n" );
document.write( "card is  which equals \r\n" );
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document.write( "That's close to 0.55\r\n" );
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document.write( "Edwin

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