This multi-case study examined high school students’ probability literacy, with focus on randomness, independence, and sample space. Task-based interviews were used with ten high school students. A Levels of Understanding Matrix (LUM), that was created based on pilot data using known literature, was deployed to gauge the students' understanding of randomness, independence and sample space. All data was processed through the LUM to create a consistent analysis while also providing a means to group the students into groups: Beginner, Intermediate, and Advanced. Each group held common characteristics such as the Advanced group’s ability to build and use sample space while the Beginner group did not do either. The Intermediate group could use the sample space with some prompting. More general results show that students do not access positive or negative recency when dealing with random events but are still developing their understanding of randomness as an unordered list. Students used representativeness when dealing with independence while mostly being able to identify separate events. Further, when students could create and use sample spaces, their apparent understanding of randomness, and to a lesser extent independence, was more developed. Lastly, it was found that students did not see outcomes as independent when there was the perception that skill was a factor in the activity, such as basketball. Students viewed the trials as being related since the basketball player was building skill as he or she played the game. The study indicates that developing and using the sample space plays a key role in students’ understanding and should be a focus of teaching.