Probability and Combinatorics
FREE online course  Learn basics in probability and combinatorics to make good decisions about the occurrence of events
Description
With this free online course you will master the skills necessary to make sound decisions about the chances of specific events occurring.
You will begin by learning how to evaluate factorial notation and methods to represent relationships using sample spaces, tree diagrams and Venn diagrams.
From there, move on to study the differences between a permutation and a combination and learn how to make adjustments for a variety of situations. What happens when there are duplicate objects in the experiment? What happens if objects are or are not replaced in the experiment? What happens when you are using all or only some of the objects in the experiment? Each of these situations will be explained and demonstrated with examples.
Then the Fundamental Counting Principle will be used to introduce the Probability Principle. Investigate the numerical range of values for various probabilities – including the probability of an “impossible” event occurring and the probability of a guaranteed or “certainty” event occurring.
You will explore how to find the probabilities of mutually exclusive and mutually inclusive events, independent and dependent events, and probabilities of more than one event occurring “with replacement” or “without replacement." Conditional probabilities will also be defined and further illustrated with examples.
Finally, a Bernoulli experiment, where there are only two possible outcomes, will be defined and the requirements for its use explained. Explore how to compute the probability of a Bernoulli experiment for exactly ‘x’ or at least ‘x’ successes and then move on to the Binomial Theorem and Pascal’s Triangle. Learn how to expand binomials using both tools and how to find a specific term in the expansion.
Start Course NowModules
Permutations and the Fundamental Counting Principle

Permutations and the Fundamental Counting Principle: Learning Outcomes

Permutations  Vocabulary and Notations

Evaluating Permutations

Permutations without Repetitions

Permutations with Repetitions
Combinations
Probability  An Introduction

Probability  An Introduction: Learning Outcomes

An Introduction to Probability

Sample Spaces

Tree Diagrams

Venn Diagrams
Types of Probability

Types of Probability: Learning Outcomes

An Introduction to Types of Probability

Empirical Probability

Theoretical Probability
Evaluating Probabilities

Evaluating Probabilities: Learning Outcomes

Evaluating Probabilities

Certainties and Impossibilities

Simple Probabilities
The Probability of Mutually Exclusive or Inclusive Events

The Probability of Mutually Exclusive or Inclusive Events: Learning Outcomes

The Probability of Mutually Exclusive Events

The Probability of Mutually Inclusive Events
The Fundamental Counting and Probability Principles

The Fundamental Counting and Probability Principles: Learning Outcomes

The Counting Principle

The Probability Principle
The Probability of Independent and Dependent Events

The Probability of Independent and Dependent Events: Learning Outcomes

The Probability of Independent Events

The Probability of Dependent Events
Bernoulli Experiments

Bernoulli Experiments: Learning Outcomes

An Introduction to Bernoulli Experiments

Exactly 'x' Successes in 'n' Trials

At least 'x' or At most 'x' Successes in 'n' Trials
The Binomial Theorem and Pascal's Triangle

The Binomial Theorem and Pascal's Triangle: Learning Outcomes

The Binomial Theorem

Binomial Expansion and Pattern of the Variables

Pascal’s Triangle

Binomial Expansion with Coefficients

Finding the 'rth' Term of a Binomial Expansion
Conditional Probabilities

Conditional Probabilities: Learning Outcomes

Conditional Probability

Conditional Probability Examples
Summary of Major Course Formulas and Ideas
Course assessment
Learning Outcomes
Having completed this course, students will be able to :
 Explain/compute factorials
 Distinguish permutation from combination and state definitions
 Compute permutations with or without replacement, duplicate objects, and using all or some of the objects
 Explain differences between impossible/certain events and their probabilities
 Compare sample spaces, tree and Venn diagrams
 Compare empirical and theoretical probabilities
 Compute mutually exclusive/inclusive event probabilities
 Explain Counting/Probability Principles for independent/ dependent events
 Differentiate probabilities of more than one event occurring “with replacement” or “without replacement and compute values
 Summarize Bernoulli experiments and requirements
 Relate Binomial Theorem/Pascal’s Triangle to expand binomials and find a specific term
 Explain meaning of and compute conditional probabilities
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
Ideal for sharing with potential employers  include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
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