The student demonstrates a consistent and correct use of mathematical notation, symbols, and terminology, particularly in relation to probability concepts such as mutual exclusiveness and binomial coefficient. They provide detailed definitions for additional terms, such as the Random Match Probability, in appropriate places within the exploration. The use of deductive reasoning is evident throughout, as the student sets out logical proofs, for example, in the context of the FBI's system and the findings of Troyer. Additionally, the student appropriately labels graphs, tables, and diagrams at the bottom. However, there are areas for improvement, as key terms and variables are not defined and explained when first introduced, and the main concepts, such as the mathematics behind the Birthday Problem, are not adequately described in the introduction. Furthermore, the degree of accuracy for rounded values is not consistently stated, and the rounded results are not always clearly indicated as such.
