Question

Consider the domain of dealing five-card poker hands from a standard deck of 52 cards, under the assumption that the dealer is fair. What is the probability of each atomic event?

Answer 1

a. The number of "microstates" for the cards that come up from five random cards each from a separate deck is 52 C 5. b. The probability of getting 5 queens of hearts is 1 / 2,598,960. c. The probability of getting any specific hand of five cards is 1 / 2,598,960.

Step-by-step explanation:

a. To calculate the number of "microstates" for the cards that come up from five random cards each from a separate deck, we use the formula for combinations. There are 52 cards in a deck and we want to choose 5 cards, so the number of microstates is 52 C 5. Using the formula, this is equal to 52! / (5! * (52-5)!), which simplifies to 2,598,960.

b. The probability of getting 5 queens of hearts is extremely low since there is only one queen of hearts in a standard deck. The probability is 1 / 2,598,960.

c. The probability of getting any specific hand of five cards is also extremely low. The number of possible hands is 52 C 5, which is 2,598,960. So the probability of getting a specific hand is 1 / 2,598,960.