Final answer:
The most probable distribution for a system of N independent, distinguishable particles, each of which can be in one of two states, is described by the Bose-Einstein distribution. In this distribution, the particles are evenly distributed between the boxes, with each box containing two particles.
Step-by-step explanation:
The most probable distribution for a system of N independent, distinguishable particles, each of which can be in one of two states, is described by the Bose-Einstein distribution.
In this distribution, the particles are evenly distributed between the boxes, with each box containing two particles. The probability of finding the system in this configuration is determined by the number of microstates within the distribution, which is proportional to the entropy of the system.
The least probable configuration is when all four particles are in one box, corresponding to other distributions such as the Binomial distribution. The probability of finding all particles in only one box is much lower, with a probability of approximately 16.