Final answer:
The probability of the system operating under the condition shown is 0.40, with an equal distribution of particles between the two boxes. The least probable configuration is having all particles in one box, with a probability of 0.16.
Step-by-step explanation:
The probability that the system will operate under the condition shown, where all four particles are evenly distributed between the two boxes, is 0.40. This is the most probable configuration for the system. The least probable configuration is one in which all four particles are in one box, with a probability of 0.16. The probability of finding all particles in only one box (either the left or right box) is also 0.16.