Discrete Mathematics & Probability Basics

This module introduces the discrete tools used across mathematics, computing and the sciences, with a careful treatment of counting, probability and elementary logic. Learners build fluency with permutations, combinations and the probability axioms, then apply them to conditional probability, independence and simple distributions. Logical reasoning and set-based language underpin the whole module. By its end, learners can analyse a counting or probability problem with structure and precision.

Learning Outcomes

Apply the fundamental counting principle to problems involving arrangements and selections (apply)

Compute permutations and combinations and distinguish when each is appropriate (apply)

Evaluate probabilities of simple and compound events from the axioms (apply)

Compute and interpret conditional probability and independence (apply)

Analyse set-based statements using union, intersection and complement (analyse)

Construct truth tables and simplify propositional statements (create)

Evaluate the validity of a probabilistic argument (evaluate)

Model a real situation using a discrete probability distribution (create)

Topics Covered

Sets, Venn diagrams and set operations

Propositional logic and truth tables

The fundamental counting principle

Permutations and factorial notation

Combinations and the binomial coefficient

The binomial theorem

Sample space and probability axioms

Addition rule and mutually exclusive events

Multiplication rule and independence

Conditional probability

Bayes' theorem (introductory)

Discrete random variables and expectation

Simple probability distributions

Counting problems in context

Introduction to graphs and trees

Skills Developed

Counting arrangements and selections Working with factorials and binomial coefficients Translating problems into set/probability language Computing conditional probabilities Constructing and reading truth tables Applying the binomial theorem Modelling with discrete distributions Reasoning about independence

Suggested Resources

STRAIT Discrete Mathematics workbook (TutorDA, 2025)

Rosen, K. Discrete Mathematics and its Applications (8th ed.), chapters 1-7

Grimaldi, R. Discrete and Combinatorial Mathematics

Khan Academy: Probability and Combinatorics playlist

Brilliant.org: Introduction to Probability

GeoGebra probability simulator

TutorDA practice bank: A-M5 drill sets

Assessment

Assessment splits a timed exam that stresses correct application of counting and probability rules with a project in which learners analyse a discrete model of a real scenario.

Written examination (2 hr)55%

Project and problem sets45%

Practice bank: 200 MCQs · Timed mock & self-paced modes

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