How can teachers build notions of conditional probability and independence?

The focus of this chapter is on research in conditional probability and independence that uses both with- and without-replacement tasks. Probabilistic thinking about conditional occurrences as well as independence are explored. A framework postulates that middle school students' thinking in conditional probability and independence could be described and predicted across four levels that represent a continuum from subjective thinking to numerical reasoning. Then implications for teaching and learning are considered, emphasizing the fostering of understanding.