Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and non-mutually exclusive events. The distinction between contradictions and contraries is explained and examples using dice are described which can be used by teachers to help students understand their differences. The second section deals with independent versus dependent events. Some common misunderstandings are presented which relate to these terms, and sample teaching activities are suggested. The final section deals with the confusion some students have when attempting to differentiate between independent events and exclusive events. (TW)