Why are apparent violations of the second law extremely unlikely in a glass of water?

Apparent violations of the second law of thermodynamics in a glass of water are not impossible, but they are exceedingly improbable.12

The second law is statistical in nature. At the microscopic level, individual molecular collisions are reversible, meaning there is no fundamental physical law preventing a chance event where slow-moving (cold) molecules collect in one area to form ice while the surrounding water becomes hotter.132

However, a glass of water contains an enormous number of molecules—approximately ${10}^{24}$—making it highly unlikely that a significant fraction of these molecules would spontaneously organize in such a way. While such a fluctuation is not strictly impossible, the probability is so low that an observer would have to wait many times the age of the universe to witness it. Consequently, for macroscopic systems, the second law is considered essentially exact.12