## ABSTRACT

Probability is introduced by considering equally likely outcomes of digits from 0 to 9 on a decagonal spinner, and applications to random number generation and drawing simple random samples. The relative frequency and subjective interpretations of probability are discussed along with the addition rule, conditional probability and the multiplicative rule which are covered using Venn diagrams and tree diagrams. The axioms of probability are stated and related to these rules. Applications of probability are given and include Bayes’s rule, in particular in the context of diagnostic testing, and decision trees. Permutations and combinations are explained and simple random sampling is defined. Two experiments are linked to this chapter: a scoring rule for validating subjective probabilities; and Buffon’s needle for showing how relative frequencies approximate probabilities and can be used to estimate the value of pi. MATLAB and R are used for numerical calculations and for writing functions that can be used to investigate the effects of changing assumed probabilities. The chapter ends with a summary of: notation used; the main results, MATLAB and R syntax; and exercises.