We investigate the level of understanding of probability as related to games and gambling, and the concept of independence of events using a convenience sample of college undergraduates taking an introductory course in applied business statistics. We examined the students' perception of the role of skill in winning at four different games through an in-class assessment, after the introduction of the concepts of elementary probability and independence of events. While the students had been instructed and tested on their ability to assess basic probability problems and independence of events in applied business examples, a larger than expected number still had trouble with questions utilizing the same concepts but with differing applications.