When rolling two six-sided dice, the possible outcomes for each die range from 1 to 6. To achieve a sum of 3, there are specifically two combinations of face values that can result in this outcome. These combinations represent different ways to roll the dice but lead to the same sum, and they are known as microstates.
The two microstates that lead to the macrostate of rolling a total of 3 are:
- Dice 1 shows 1 and Dice 2 shows 2 (1 + 2 = 3)
- Dice 1 shows 2 and Dice 2 shows 1 (2 + 1 = 3)
Thus, while the macrostate description focuses on the outcome (the sum of 3), these two distinct arrangements (microstates) showcase the different ways to achieve that same total. It’s important to understand that in probability and statistics, each unique arrangement that results in the same outcome contributes to our overall understanding of events when rolling dice.
So, in summary, for the outcome of a sum of 3 when rolling two dice, there are 2 possible microstates:
- (1, 2)
- (2, 1)
This concept helps us appreciate the richness of possibilities in simple games of chance, as well as the foundational principles in probability theory.