Assessing Students' Difficulties with Conditional Probability and Bayesian Reasoning

In this paper we first describe the process of building a questionnaire directed to globally assess formal understanding of conditional probability and the psychological biases related to this concept. We then present results from applying the questionnaire to a sample of 414 students, after they had been taught the topic. Finally, we use Factor Analysis to show that formal knowledge of conditional probability in these students was unrelated to the different biases in conditional probability reasoning. These biases also appeared unrelated in our sample. We conclude with some recommendations about how to improve the teaching of conditional probability.