  We report on the development of students' ideas of probability and
probability density in a University of Maine laboratory-based general education
physics course called Intuitive Quantum Physics. Students in the course are
generally math phobic with unfavorable expectations about the nature of physics
and their ability to do it. We describe a set of activities used to teach
concepts of probability and probability density. Rudimentary knowledge of
mechanics is needed for one activity, but otherwise the material requires no
additional preparation. Extensions of the activities include relating
probability density to potential energy graphs for certain "touchstone"
examples. Students have difficulties learning the target concepts, such as
comparing the ratio of time in a region to total time in all regions. Instead,
they often focus on edge effects, pattern match to previously studied
situations, reason about necessary but incomplete macroscopic elements of the
system, use the gambler's fallacy, and use expectations about ensemble results
rather than expectation values to predict future events. We map the development
of their thinking to provide examples of problems rather than evidence of a
curriculum's success.
