An understanding of conditional probability is essential for students of inferential statistics as it is used in Null Hypothesis Tests. Conditional probability is also used in Bayes' theorem, in the interpretation of medical screening tests and in quality control procedures. This study examines the understanding of conditional probability of students entering an introductory applied statistics unit at an Australian university. These students answered questions that tested their ability to interpret conditional statements in two-way tables and their ability to discern the difference between a conditional statement and its inverse in written form. They also answered questions to determine if they held the time-axis fallacy.