Can entropy ever be reduced by random chance?

Measure of a system's energy that is unavailable for work, or of the degree of a system's disorder. When heat is added to a system held at constant temperature, the change in entropy is related to the change in energy, the pressure, the temperature, and the change in volume. Its magnitude varies from zero to the total amount of energy in a system. The concept, first proposed in 1850 by the German physicist Rudolf Clausius (1822 – 1888), is sometimes presented as the second law of thermodynamics, which states that entropy increases during irreversible processes such as spontaneous mixing of hot and cold gases, uncontrolled expansion of a gas into a vacuum, and combustion of fuel. In popular, nontechnical use, entropy is regarded as a measure of the chaos or randomness of a system.

Sure it can. Nothing says that entropy can not be reduced...ie negative. What the laws do say is that in a closed system entropy has to always increase.

A cup of coffe for instance is not a closed system. ie heat and mass can flow in and out of the cup. The entropy of the cup of cofffe decreases nicely. But, ..something else happens..the entropy in the room increases. If the rom where a closed system then production in the room casued by the flow of heat into the room. The procution in the room plus entropy decrease in the cup will sum up to an overall increase in entropy even though the cup itself decreased

No.