Question

In the card game of poker, you are dealt 5 cards out of the 52 card deck. A deck of cards consists of four suits (hearts, diamonds, spades, clubs), with each suit consisting of the ranks Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King. You have a "four of a kind" in your hand if you have all cards of the same rank in your hand (examples include four Aces, four Queens, or four sixes). Give an expression for the probability you are dealt a "four of a kind".

Answer 1

The probability of being dealt a 'four of a kind' in poker involves calculating the combinations for four cards of the same rank and one additional card from the remaining cards.

Step-by-step explanation:

The probability of being dealt a four of a kind in a game of poker can be calculated by considering the ways to choose the four cards of the same rank and the final fifth card of a different rank. To calculate this probability, you should first determine the number of possible ways to get four of a kind out of 52 cards. There are 13 different ranks and for each rank, you can choose 4 cards in 1 way since you have to take all 4 cards of the same rank. After picking four cards of one rank, the remaining 1 card can be any one of the other 48 cards that are not of the same rank.