STATS 125 : Probability and its Applications


2023 Semester Two (1235) (15 POINTS)

Course Prescription

Probability, conditional probability, Bayes theorem, random walks, Markov chains, probability models. Illustrations will be drawn from a wide variety of applications including: finance and economics; biology; telecommunications, networks; games, gambling and risk.

Course Overview

The course concentrates on probability models and their applications in a variety of fields. Probability underpins both statistics and (stochastic) operations research. As such, this is a core course for students in the Statistics and Probability pathway or a Data Science Specialisation, and optional for those pursuing the Applied Statistics pathway or a Statistics major.  Probability models are also used in disciplines as varied as Commerce and Biology (e.g., calculating the probability that a share price will exceed a certain level or the probability that a population will become extinct). This means the course is useful for students with varied interests, as well as those who have Maths or Statistics as their main interest. STATS 125 is a prerequisite for STATS 210. Students with a weak mathematics background will need to pass MATHS 102 before taking STATS 125 and MATHS 108.

The course covers four broad areas (roughly one quarter each): Probability, Discrete distributions, Joint and conditional distributions, and Markov chains. Illustrations will be drawn from a wide variety of applications including finance and economics, genetics, bioinformatics and other areas of biology, telecommunication networks, games, gambling and risk, and forensic science.

Course Requirements

Corequisite: ENGSCI 111 or MATHS 108 or 110 or 120 or 130 Restriction: STATS 210

Capabilities Developed in this Course

Capability 1: Disciplinary Knowledge and Practice
Capability 2: Critical Thinking
Capability 3: Solution Seeking
Capability 4: Communication and Engagement
Graduate Profile: Bachelor of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Demonstrate the use of probability rules, discrete distributions, joint distributions and Markov chains to solve problems (Capability 1 and 3)
  2. Translate information given in words into correct probability statements (Capability 1 and 3)
  3. Select an appropriate discrete probability model to solve a problem (Capability 1 and 3)
  4. Produce and clearly explain mathematical calculations and reasoning (Capability 1, 3 and 4)
  5. Interpret their solution to a probability problem with reference to the context of the problem (Capability 1 and 4)
  6. Recognise and specify the limitations of a simple probability model in a given context (Capability 1 and 2)
  7. Differentiate between reasonable and unreasonable solutions to probability problems (Capability 1, 2 and 3)


Assessment Type Percentage Classification
Assignments 18% Individual Coursework
Tutorials 12% Individual Coursework
Online Test 20% Individual Coursework
Final Exam 50% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7
Online Test
Final Exam

45% in the final exam as well as 50% overall is required to pass.


Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at

Statistics has a Tuākana Programme where there is a workspace and a social space shared with Science Tuakana students. Tutorials and one-to-one assistance are available. Tuākana tutors/mentors work alongside the lecturer to support students with assignments and revision for the quizzes and exams. For more information and to find contact details for the Statistics Tuākana coordinator, please see

Contacts are Susan Wingfield ( and Heti Afimeimounga (

Key Topics

  • Probability
  • Conditional probability
  • Bayes' theorem
  • Discrete distributions
  • Expectation and variance
  • Joint and conditional discrete distributions
  • Definition and examples of Markov chains
  • Random walks
  • Hitting probabilities and times
  • Equilibrium distributions

Special Requirements

The mid-semester online test will be held in the evening. The date and time will be advised on Canvas at the beginning of the semester.

Workload Expectations

This course is a standard 15-point course and students are expected to spend 150 hours per semester involved in each 15-point course that they are enrolled in.

For this course, a typical weekly workload includes:

  • 3 hours of lectures
  • A 1-hour tutorial
  • 3 hours of reading and thinking about the content
  • 5-6 hours of work on assignments and/or test preparation

Delivery Mode

Campus Experience & Campus Experience

This course is available for remote students.

Attendance is expected at scheduled activities including tutorials to complete components of the course.
Lectures will be available as recordings. Other learning activities including tutorials will not be available as recordings.
The course may include live online events including group discussions and tutorials.
Attendance on campus is not required for the test. 

The activities for the course are scheduled as a standard weekly timetable.

Learning Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

  • The coursebook contains all the notes and most examples covered in class plus additional practice exercises. 
  • A pdf copy is available on Canvas.
  • It is assumed that students have access to a scientific (or graphics) calculator.

Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

There will be ongoing review of tutorial content and delivery.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.

Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.


The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website

Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page

This should be done as soon as possible and no later than seven days after the affected test or exam date.

Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter


Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 01/11/2022 09:37 a.m.