Question

Suppose you select four cards at random from a standard deck of playing cards and end up with a macrostate of four deuces. How many microstates are associated with this macrostate?

Answer 1

There is only one microstate associated with the macrostate of drawing four deuces from a deck of cards because there is one deuce in each suit, and no additional combinations exist for this specific hand.

Step-by-step explanation:

The concept of microstates and macrostates can be applied to a deck of playing cards to illustrate probability and entropy. For the case of drawing four deuces from a standard deck of playing cards, the macrostate is defined as having all four cards be deuces.

In terms of microstates, there is only one possible combination of four deuces because there is exactly one deuce in each of the four suits: clubs, diamonds, hearts, and spades. Hence, the number of microstates corresponding to the macrostate of four deuces is exactly one.

Since each card is unique in its suit and rank, the differentiation between the cards does not lead to any additional microstates in this specific scenario. The concept of entropy is also relevant here because a hand with a high level of order, such as four deuces, has a low entropy, while a more disordered hand would have a higher entropy.

Answer 2

There are four microstates associated with the macrostate

Step-by-step explanation:

Macrostate is the largest possible microstate outcome in an event.

There are four deuces in a standard deck of playing cards, these include;

two heart, two spade, two club and two diamond.

Thus, when a macrostate of four deuces are selected, the microstates are two heart, two spade, two club and two diamond.

The microstates are four.

Therefore, there are four microstates associated with the macrostate.