1. The problem statement, all variables and given/known data If you have a three energy level system, with energies 0, A, B where B>A, which consists of only two particles what is the probability that 1 of the particles is in the ground state? What about if two of them are in the ground state? Do this using both fermi and boson statistics. 2. Relevant equations Using Fermi-statistics, Z=exp(-β*A)+exp(-β*B)+exp(-β*(A+B)) Using Boson statistics, Z=1+exp(-β*A)+exp(-2 β*A)+exp(-β*B)+exp(-2 β*B)+exp(-β*(A+B)) 3. The attempt at a solution For 1 particle in the ground state, In fermi statistics there are two arrangments which satisfy this condition, when 1 particle is in the ground state and the other in A, and when the other is in B. P = Pg(Pa+Pb) = (1/Z)(exp(-β*A)/Z + exp(-β*B)/Z) Does that look correct? Would be a similar answer for boson statistics, just with the different partition function. For both particles in the ground state Fermi: P = Pg1 Pg2 = (1/Z)(1/Z) = Z-2 This doesn't look correct, the answer should be zero because fermions cant be in the same energy level.. Can anyone see what I have done wrong? Boson is the same answer with the different partition function, though its correct that the answer is non-zero here. Have I done the probabilities incorrectly?