A system has three macrostates. Macrostates 1 and 3 are least likely and have one basic state each. Macrostate 2 is the equilibrium state and is three times more likely to occur than either of the other two macrostates.

Part A) What is the probability that the equilibrium state 2 occurs?

Part B) What is the probability that microstate 1 or 3 occurs?

a) 0.6

b) 0.4

Explanation:

The number of states available in macrostate 1 = 1 basic state

The number of states in macrostate 3 = 1 basic state too

But the number of states of macrostate 2 = 3 * (number of states in either of the macrostate 1 or 3) = 3 * 1 = 3

Total number of states available in the macrostates = 1+3+1 = 5

a) probability that the equilibrium state 2 occurs = (number of states available in equilibrium 2) / (total number of states) = (3/5) = 0.60

b) probability that microstate 1 or 3 occurs = (number of states available in microstate 1 or 3) / (total number of states) = 2/5 = 0.4