### Abstract:

The purpose of this descriptive case study analysis was to provide portraits of the
methods college students used to solve probability problems and the factors that
supported or impeded their success prior to and after two-week instruction on probability.
Fourteen-question Pre- and Post-Instructional Task-Based Questionnaires provided
verbal data of nine participants enrolled in a college finite mathematics course while
solving problems containing simple, compound, independent, and dependent probabilistic
events.
Overall, the general method modeled by the more successful students consisted of
the student reading the entire problem, including the question; breaking down the
problem into sections, analyzing each section separately; using the context of the
question to reason a solution; and checking the final answer. However, this ideal method
was not always successful. While some less successful students tried to use this approach
when solving their problems, their inability to work with percents and fractions, to
organize and analyze data within their own representation (Venn diagram, tree diagram,
table, or formula), and to relate the process of solving word problems to the context of the
problem hindered their success solving the problem. In addition, the more successful
student exhibited the discipline to attend the class, to try their homework problems
throughout the section on probability, and to seek outside help when they did not
understand a problem.
However, students did try alternate unsuccessful methods when attempting to
solve probability problems. While one student provided answers to the problems based
on his personal experience with the situation, other students sought key words within the
problem to prompt them to use a correct representation or formula, without evidence of
the student trying to interpret the problem. While most students recognized dependent
events, they encountered difficulty stating the probability of a dependent event due to
their weakness in basic counting principles to find the size of the sample space. For those
students who had not encountered probability problems before the first questionnaire,
some students were able to make connections between probability and percent. Finally,
other inexperienced students encountered difficulty interpreting the terminology
associated with the problems, solving the problem based on their own interpretations.