Abstract
A probabilistic reasoning hierarchy for the concepts of sample space and the probability of a compound event is proposed as a tool to describe high-school students’ performance when solving two problems involving binomial experiments , before and after a period of teaching. As expected, the responses to the post-tests indicate an improvement in the levels of reasoning in comparison with the pre-test results. In the pre-test, list and tables were the most frequently used procedures to count sample space elements and to compute the probabilities of compound events. In the post-test, the most common strategies were enumeration, tree diagrams, and use of the product rule. Tree diagrams were a useful tool in improving the students’ probabilistic reasoning.
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Notes
- 1.
We consider compound events to be events such as “A or B,” “A and B,” and “the complement of A.” In this chapter, we use compound events consisting of pairs or trios of outcomes (e.g., Girl-Girl, Even-Even-Even).
- 2.
According to Yates et al. (2003, p. 439), a binomial experimental setting is a situation where the following conditions are satisfied: (1) Each observation (trial) falls into one of just two categories (“success” or “failure”); (2) there is a fixed number of independent observations; and (3) the probability of success (p) is the same for each observation .
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Landín, P., Salinas, J. (2018). Students’ Reasoning About Sample Space and Probabilities of Compound Events. In: Batanero, C., Chernoff, E. (eds) Teaching and Learning Stochastics. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-72871-1_14
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