Conditional probabilities: Insights and difficulties

Conditional probabilities play a central role in the process of inferring about the uncertain world. The formal definition of P ( A / B ) is easy and poses no problems. However, upon careful probing into students' ideas of conditional probabilities, some misconceptions and fallacies are uncovered. In this paper I wish to discuss three issues involving conditional probabilities that I believe require serious consideration and clarification by students and by teachers of probability. These issues are: Interpreting conditionality as causality, problems with defining the conditioning event, and confusion of the inverse.