STATS 125 : Probability and its Applications


2021 Semester One (1213) (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 take (and pass) MATHS 102 before taking STATS 125 and MATHS 108.

Topics covered are 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. 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: 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
Quizzes 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

Minimum of 45%  in the final exam (as well as 50% overall) required to pass.


The Department of Statistics has a team of eight Tuākana tutors covering our Stage 1 and Stage 2 courses, including STATS 125. For details and online session times, visit

Key Topics

The course covers four broad areas (roughly one quarter each):  Probability, Discrete distributions, Joint and conditional distributions, and Markov chains.

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 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, you can expect 3 hours of lectures, a 1-hour tutorial, 3 hours of reading and thinking about the content and 5-6 hours of work on assignments, quizzes and/or test or exam preparation, each week.

Delivery Mode

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

The course book contains all the notes and most examples covered in class plus additional practice exercises.  The Course book is available for purchase from the Science Student's resource centre. 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.

Digital 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.

A digital copy of the coursebook (as printed with gaps to complete in lectures)  and a filled-in version are both available on Canvas. 

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.


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 your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.

Level 1: Delivered normally as specified in delivery mode
Level 2: You will not be required to attend in person. All teaching and assessment will have a remote option. The following activities may also have an on campus / in person option: Lectures,  tutorials, office hours.
Level 3 / 4: All teaching activities and assessments are delivered remotely

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 you may be asked to submit your 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. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.

Published on 10/01/2021 06:46 p.m.