(Solved): 2) Consider systems A and B in thermal contact. System A is a "two-part" and system B a "four-p ...

2) Consider systems A and B in thermal contact. System A is a "two-part" and system B a "four-part" system. A has two distinguishable particles, each with non-degenerate states containing energies $0,?,2?,3?$ and $\mathrm{B}$ has four distinguishable particles, each having nondegenerate states containing energies $0,?,2?,3?$. The total energy $\mathrm{E}=3?$. (a) Calculate the probability for (i) All energy $(3?)$ to be in system A. (ii) All energy $(3?)$ to be in system B. (iii) System A to have an energy $?$ and system B to have an energy $2?$. (iv) System B to have an energy $2?$ and system B to have an energy $?$. (b) What is the sum of your answers in (i)-(iv). Why? (c) Calculate the average energy in system A using (i)-(iv). Was this result expected?