Common difficulties with probabilistic reasoning

In the past two decades several influential organizations, including the national Council of Supervisors of Mathematics, NACOME, UNESCO, CEEB, and the Cambridge Conference on School Mathematics, have acknowledged the role that probability and statistics play in our society. Consequently, each has recommended that probability and statistics be included as part of the modern mathematics curriculum. Probabilistic reasoning may not be an easily acquired skill for most students, however. Several recent studies have reported that even after instruction, many students have difficulties developing an intuition about the fundamental ideas of probability. Without this intuition they fail miserably when forced to reason about probable events.