To calculate the probability that both particles are in the same half of the container, we can use the canonical ensemble in statistical mechanics. The canonical ensemble is a statistical ensemble representing the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature.Let's consider a 1-dimensional container of length L. We can divide the container into two halves, each of length L/2. We want to find the probability that both particles are in the same half of the container.First, we need to find the total number of possible microstates for the two particles in the container. Since the particles are indistinguishable, we can consider the number of ways to arrange the particles in the container as the number of ways to divide the container into two equal parts. This can be done in two ways: either both particles are in the left half or both particles are in the right half.Now, let's find the total number of microstates for the system. Since the particles are indistinguishable and can be anywhere in the container, the total number of microstates is equal to the number of ways to divide the container into two equal parts, which is 2.The probability of both particles being in the same half of the container is the ratio of the number of microstates where both particles are in the same half to the total number of microstates:P same half = number of microstates with both particles in the same half / total number of microstates P same half = 2 / 2 = 1So, the probability that both particles are in the same half of the container is 1, or 100%. However, this result is not physically accurate, as it assumes that the particles are indistinguishable and can be anywhere in the container without any restrictions. In reality, the probability would be less than 100% due to the particles being distinguishable and having restrictions on their positions and velocities due to temperature and other factors.