Find the probability of drawing a full house from a set of 52 cards?

MAth problem above. Thanks

4 Answers

Relevance
  • QC
    Lv 7
    8 years ago
    Favorite Answer

    Total number of hands: (52 C 5) = 2,598,960

    Full house: 3 of a kind + 2 of a kind

    3 of a kind could be one of 13 different values

    For each of these, there are (4 C 3) ways to choose 3 cards

    2 of a kind could be one of 12 remaining values

    For each of these, there are (4 C 2) ways to choose 2 cards

    Number of hands that are full houses

    = 13 * (4 C 3) * 12 * (4 C 2) = 13*4 * 12*6 = 3744

    Probability of drawing a full house = 3744/2,598,960 = 0.001440576 = 0.144%

  • Anonymous
    8 years ago

    ok thre is 52 cards and there are 4 of each number so you would divide 52 by 4 and get 13 so that means there are 13 cards for each set not you would times 52 and 13 and get 676, so there are 676 different ways to get a full house. is that what your asking for?

  • 3 years ago

    The are 4 aces in a properly-recognized deck of fifty two taking part in cards. So on a single draw (if the deck is complete) you have a 4 in fifty two possibility of pulling an ace, which reduces to one million in 13. precis: one million in 13 (or 4 in fifty two) this is a 7.6923% possibility.

  • 8 years ago

    This is a product of combinatorics.

    A full house is 3 of a kind and 2 of a kind e.g. 77733

    How many ways can you pick the first card: 13C1 = 13

    How many ways can you get 3 more of the same card: 4C3 = 4

    How many ways can you pick the other kind: 12C1 = 12

    How many ways can you get 2 more of the same card: 4C2 = 6

    Multiply these out: 3744.

    How many different hands can be dealt 52C5 = 2,598,960

    The quotient of these two is 0.144 %

Still have questions? Get your answers by asking now.