Final answer:
The probability of drawing the king of hearts at the turn in a game of Texas Hold'em after the flop is 1 in 47, since one king of hearts is the only card that fits the requirement out of the 47 unseen cards remaining in the deck. Thus, the probability of getting the king of hearts at the turn is 1/47 or approximately 2.13%.
Step-by-step explanation:
The subject of this question is Mathematics, specifically the area of probability as it pertains to card games like Texas Hold'em. You're playing Texas Hold'em against the dealer and currently holding the 9 and 10 of hearts. The dealer flops the 3 of clubs, jack of hearts, and queen of hearts. You are looking for the probability of getting the king of hearts at the turn, which is the fourth card drawn by the dealer.
In a standard deck, there are 52 cards, and 5 cards have already been seen (your two cards and the three flop cards). This leaves 47 cards unseen. Among these remaining cards, there is only one king of hearts. Therefore, the probability of drawing the king of hearts next is 1 out of 47.
Step-by-step calculation:
- Identify the total number of unseen cards: 52 (total) - 5 (seen) = 47 (unseen).
- Identify the number of cards that would fulfill your requirement: 1 (king of hearts).
- Calculate probability: Probability = Desired outcome / Total number of possible outcomes = 1/47.
Thus, the probability of getting the king of hearts at the turn is 1/47 or approximately 2.13%.