This question from my course got me confused.
Consider a system of two Einstein solids, A and B, each containing 10 oscillators, sharing a total of 20 units of energy. Assume that the solids are weakly coupled, and that the total energy is fixed.
(c) Assuming that this system is in thermal equilibrium, what is the probability of finding all the energy in solid A?
I know the answer already: it's the amount of microstates where everything is in A divided by the total amount of microstates. 20 over 29 / 20 over 39
Intuitively, I would say it's (1/2)^20 because every unit has .5 chance to be in A as well as in B. And the position of every unit is independent of other units's positions. Where am I wrong?