When the weather forecast says the day will be predominantly sunny, that means it will be mostly sunny.
Like the word dominate, predominantly comes from the Latin dominari meaning "to rule, dominate, govern." Use predominantly to describe the general, ruling quality of something, the same way you'd use the phrase "for the most part." An actor who is predominantly in films, appears mostly in movies, but might sometimes do live theater or TV. A neighborhood that is predominantly Indian has mostly Indian people living there, but maybe other groups too, in smaller numbers.
