Probability and Combinatorics | Free Online Course | Alison

Probability and Combinatorics

FREE online course - Learn basics in probability and combinatorics to make good decisions about the occurrence of events

Free Course
With this FREE online course, master the tools needed to understand probabilities in sports, business and other fields that require you to make sound decisions based on chance. Learn about factorial notation, outcome representations, permutations, combinations, The Fundamental Counting and Probability Principles, and conditional probabilities. The Bernouilli experiment, Pascal's Triangle and the Binomial Theorem will also be explained.
  • Duration

    3-4 Hours
  • Assessment

  • Certification

  • Responsive

  • Publisher






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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.

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Permutations and the Fundamental Counting Principle


Probability - An Introduction

Types of Probability

Evaluating Probabilities

The Probability of Mutually Exclusive or Inclusive Events

The Fundamental Counting and Probability Principles

The Probability of Independent and Dependent Events

Bernoulli Experiments

The Binomial Theorem and Pascal's Triangle

Conditional Probabilities

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


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:

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