Question

Five cards are selected from 52-card deck for a poker hand. You have a poker hand containing “four of a kind” —a card with the same face value in each of the four suits.

Answer 1

To find the probability of getting a four of a kind poker hand, we can use the following steps:

1. There are 13 possible card denominations (Ace, 2, 3, ..., 10, Jack, Queen, King).
2. To get a four of a kind hand, we need to choose one of these 13 denominations and then choose any four of the 4 suits for that denomination. There are 13 ways to choose the denomination and (4 choose 4) = 1 way to choose the suits.
3. After choosing the four of a kind cards, we need to choose one more card from the remaining 48 cards. There are 48 possible cards to choose from.
4. The total number of possible five-card hands is (52 choose 5) = 2,598,960.

Therefore, the probability of getting a four of a kind poker hand is:

(13 * 1 * 48) / (52 choose 5) ≈ 0.0240 or about 1 in 42.