A box initially divided into two equal halves by a partition contains some number of particles. When the partition is removed, the particles are free to move throughout the volume of the box. Assume that all the particles have an average speed that allows them to cross from one side of the box to the other every \(2.50 \mathrm{~s}\), on average. Note that this does not mean that they uniformly switch sides; it means that they move randomly in such a way that they enter a new random distribution every \(2.50 \mathrm{~s}\). Determine the probability of all particles being in the left half of the box and the average time interval required for this to happen for \((a)\) two particles and \((b)\) ten particles.