Of course, it's possible, but the chances are quite low. Cats are generally docile animals, and such behavior is more likely due to external stimuli. Under normal circumstances, cats don't attack people unprovoked. However, if we provoke a cat, or if it's nervous or acting out of self-defense in an unfamiliar environment, it might bite.
Of course, a cat's biting behavior is not static. Some cats may bite because they are impatient; others may bite when they are too excited while playing. These are all possibilities. The important thing is for us pet owners to train them.
