Probability and Combinatorics

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.