Suppose it is known that the ratio of the volume of A to that of A' = 3. Suppose further that initially, there were 500 gas X molecules and 3500 gas Y molecules in subsystem A and that there were 700 gas X molecules and 6000 gas Y molecules in A'. Once you poke a hole, these numbers will re-adjust in such a way that in equilibrium, the mean number densities of A and A' are equal. Use this fact to:

(i) Calculate the new mean number of molecules in A and A'. (ii) Evaluate the probability of finding all 4000 molecules of gas A to the left of the demarcation line and all 400 molecules to the right after the partition has been removed.