Anything done randomly has no plan or strategy. If you choose your college courses randomly, you may end up studying some unusual topics. Hope you enjoy Advanced History of Cheese-Making!
When you pick the name of a prize winner from, you're choosing randomly. In other words, there's no specific method to making the selection; you're simply grabbing a random slip of paper. Sometimes this adverb implies chaos: "Clothes were tossed randomly around her room, while a laundry basket stood empty." This haphazard sense of both randomly and random grew from the original definition, "at great speed."