Four distinguishable gas particles are initially confined to bulb A of a two-bulb apparatus consisting of identical bulbs A and B connected by a thin tube with a closed valve. The valve is then opened, allowing the particles to move freely between the bulbs. Which of the following statements correctly compares the probability \(P_{(4,0)}\) of finding all four particles in bulb A to the probability \(P_{(2,2)}\) of finding two particles in each bulb, and provides a correct explanation based on statistical mechanics?