Question

Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.

Answer 1

To calculate the "microstates" for the cards that come up from five random cards each from a separate deck, use the concept of combinations. The probability of getting 5 queens of hearts or any specific hand of five cards depends on the specific combination being considered.

Step-by-step explanation:

To calculate the "microstates" for the cards that come up from five random cards each from a separate deck, we need to calculate the number of ways we can choose 5 cards out of the 52 cards in a deck. This can be done using the concept of combinations, denoted as C(n, r), where n is the total number of cards and r is the number of cards we want to choose. The formula for combinations is:

C(n, r) = n! / (r!(n - r)!)

In this case, n = 52 and r = 5, so the number of "microstates" is:

C(52, 5) = 52! / (5!(52 - 5)!)

Next, to calculate the probability of getting 5 queens of hearts, we need to calculate the number of ways we can choose 5 queens of hearts from the deck. Since there is only 1 queen of hearts in a standard deck, the probability of choosing 5 queens of hearts is 0. The same logic applies to the probability of getting any specific hand of five cards, as it depends on the specific combination being considered.

Answer 2

2, 3, 4, 5, 6, 7, 8, 9, 10. 11. 12. 13. 13. 15. 16. 17, 18, 19, 20