Question

(a) How many "microstates" are there for the numbers that come up on a pair of dice?

(b) What is the probability that a roll of a pair of dice will show two sixes?

Short answer

(a). For a pair of dice, the possible number of microstates is$36$.

(b). Probability of six showing up on both dices is$\frac{1}{36}$ .

Step-by-step solution

Given information

(a). The microstates are there for the numbers that come up on a pair of dice.

(b). The probability that a roll of a pair of dice will show two sixes.

Concept of microstates of dice

Each possible outcome is called a “microstate”. A "microstate" is the sum of all microstates that yield the same number of spots.”. The microstates that contain the most microstates is the most probable to occur.

Calculate the number of microstates

a)

One dice has 6 possible outcomes, thus the number of microstates for a dice is 6.

For a pair of dice the possible number of microstates$=6\times 6=36$.

Calculate the probability of dice shows sixes

b)

The probability of a six come up on a dice$=1/6$.

The probability of six shows up on both dices$=1/6\times 1/6=\frac{1}{36}$.