ST1116 Probability (Part A)
Introductory description
This module runs in Term 2 and is a core or listed optional module for some degree courses (primarily in Mathematics and Computer Science) and is also available as an unusual option to students on nonlisted degrees. You may be interested in this module if you have taken the prerequisites and wish to take ST112 Probability B so that you can take further statistics modules.
Prerequisites: MA131 Analysis I AND MA132 Foundations (or equivalent)
Postrequisites: ST112 Probability B, ST104 Statistical laboratory, ST202 Stochastic Processes, ST220 Introduction to Mathematical Statistics
This module is not available to students who have their home department in Statistics, who take an equivalent module. Students who are considering transferring to a course in Data Science, Mathematics & Statistics or MORSE at the end of their first year should take this module.
Module aims
To lay the foundation for all subsequent modules in probability and statistics, by introducing the key notions of mathematical probability and developing the techniques for calculating with probabilities and expectations.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Experiments with random outcomes: the notions of events and their probability. Operations with sets and their interpretations. The addition law and axiomatic definition of a probability space.
 Simple examples of discrete probability spaces. Methods of counting: inclusionexclusion formula and multinomial coefficients. Examples including the birthday problem and coupon collecting.
 Simple examples of continuous probability spaces. Points chosen uniformly at random in space.
 Independence of events. Conditional probabilities. Simpson’s paradox. Bayes theorem.
 Binomial probabilities. The law of large numbers, Poisson and Gaussian approximations and their applications.
Learning outcomes
By the end of the module, students should be able to:
 Understand and apply in simple situations the law of large numbers, Poisson and Gaussian approximations for the Binomial distribution.
 Model simple experiments with random outcomes using mathematical probability.
 Compute probabilities by counting sample points or calculating areas/volume.
 Understand the concepts of conditional probability and independence.
Indicative reading list
View reading list on Talis Aspire
Subject specific skills
TBC
Transferable skills
TBC
Study time
Type  Required  Optional 

Lectures  15 sessions of 1 hour (25%)  2 sessions of 1 hour 
Tutorials  2 sessions of 1 hour (3%)  
Private study  37 hours (62%)  
Assessment  6 hours (10%)  
Total  60 hours 
Private study description
Weekly revision of lecture notes and materials, wider reading and practice exercises, working on problem sets and preparing for examination.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D3
Weighting  Study time  

Computer Based Assessment 1  5%  3 hours 
Multiple choice quiz which will take place during the term that the module is delivered. 

Computer Based Assessment 2  5%  3 hours 
Multiple choice quiz which will take place during the term that the module is delivered. 

Online Examination  90%  
The examination paper will contain three questions, of which the best marks of TWO questions will be used to calculate your grade. ~Platforms  Moodle 
Assessment group R
Weighting  Study time  

Online Examination  100%  
The examination paper will contain three questions, of which the best marks of TWO questions will be used to calculate your grade. ~Platforms  Moodle

Feedback on assessment
Answers to problems sets will be marked and returned to students. Tutorials provide opportunities for students to discuss the problem sets.
Solutions and cohort level feedback will be provided for the examination.
Postrequisite modules
If you pass this module, you can take:
 ST1126 Probability (Part B)
Antirequisite modules
If you take this module, you cannot also take:
 ST11512 Introduction to Probability
Courses
This module is Core for:
 Year 1 of UCSAG4G1 Undergraduate Discrete Mathematics
 Year 1 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 1 of UMAAG100 Undergraduate Mathematics (BSc)
 Year 1 of UMAAG103 Undergraduate Mathematics (MMath)
 Year 1 of UMAAG106 Undergraduate Mathematics (MMath) with Study in Europe
 Year 1 of UMAAG1NC Undergraduate Mathematics and Business Studies
 Year 1 of UMAAG1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
 Year 1 of UMAAGL11 Undergraduate Mathematics and Economics
 Year 1 of UECAGL12 Undergraduate Mathematics and Economics (with Intercalated Year)
 Year 1 of UMAAGV17 Undergraduate Mathematics and Philosophy
 Year 1 of UMAAGV18 Undergraduate Mathematics and Philosophy with Intercalated Year
 Year 1 of UMAAG101 Undergraduate Mathematics with Intercalated Year
This module is Optional for:
 Year 1 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 1 of UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 1 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)