Secondary and university students' understanding of independence and conditional probability

The primary objective of the study was to investigate the perceptions of Czech secondary and university students regarding independence in tasks involving multiple repetitions of random events and their understanding of conditional probability. The study employed a sample of 43 students, ranging in age from 15 to 23, who engaged in think-aloud interviews. The selection of eight tasks was based on existing literature.A qualitative analysis of the interview transcripts established that students encountered difficulties comprehending the concepts of independence and conditional probability, irrespective of whether they had previously undertaken a university course on probability. Notably, certain misconceptions about independence only surfaced in more challenging tasks, wherein students relied more on their intuition than their acquired knowledge. The misconceptions primarily manifested when describing the random space. The research findings have significant educational implications, which are discussed.