SOLUTION: 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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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? Found 2 solutions by Edwin McCravy, greenestamps:Answer by Edwin McCravy(20064) (Show Source):
You can put this solution on YOUR website! Three cards are dealt from a standard deck of fifty-two cards (without replacement); the probability that there is at least one face card?
The entire deck of cards are these 52:
A♥ 2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ 10♥ J♥ Q♥ K♥
A♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦
A♠ 2♠ 3♠ 4♠ 5♠ 6♠ 7♠ 8♠ 9♠ 10♠ J♠ Q♠ K♠
A♣ 2♣ 3♣ 4♣ 5♣ 6♣ 7♣ 8♣ 9♣ 10♣ J♣ Q♣ K♣
The number of ways to select ANY three cards from those 52 is
52 cards choose 3 = 52C3 = 22100 ways. That will be the denominator
of our probability before reducing.
But for the complement event, we remove the face cards, which leaves
these cards
A♥ 2♥ 3♥ 4♥ 5♥ 6♥ 7♥ 8♥ 9♥ 10♥
A♦ 2♦ 3♦ 4♦ 5♦ 6♦ 7♦ 8♦ 9♦ 10♦
A♠ 2♠ 3♠ 4♠ 5♠ 6♠ 7♠ 8♠ 9♠ 10♠
A♣ 2♣ 3♣ 4♣ 5♣ 6♣ 7♣ 8♣ 9♣ 10♣
So the numer of ways to select three cards from those 40 is
40 cards choose 3 = 40C3 = 9880
So the probability of the complement event is
9880 ways out of 22100 or which reduces to
<-- probability of complement event of dealing
NO face cards,
Therefore the probabilkity of selecting at least one face
card is which equals
That's close to 0.55
Edwin
