• Unit 5: Probability

    Probability is an important component of discrete mathematics. For instance, if you consider a population of 10 and then take four at a time, without duplicates, what is the chance that a certain combination within the subsets of four will occur? Or, given the set of all possible events, what is the chance that a certain event will occur, given that the event can result from various causes? The construction of trees and graphs , which we will discuss later, depends on the probability of combinations of events. Since we want to traverse trees and graphs in order of the most likely and most important events, we need to know probability.

    Completing this unit should take you approximately 4 hours.

    • Upon successful completion of this unit, you will be able to:

      • state the definitions of terms that apply to probability within the context of this course;
      • calculate conditional probabilities (the probability of event Y occurring if event X has already occurred);
      • compute the probability of independent events; and
      • estimate the chance of occurrence of a specific event within a collection of events.

    • 5.1: Introduction

    • 5.2: Sample Spaces, Events, and Their Probabilities

      • Sample Spaces, Events, and Their Probabilities Page

        Next, we learn about the sample spaces associated with random experiments, about the events that can occur from random experiments, and have a look at a specific event's probability of occurrence.

      • Try It Now Book

        Work these exercises to see how well you understand this material.

    • 5.3: Complements, Intersections, and Unions

      • Complements, Intersections, and Unions Page

        There are situations where a problem can be solved by representing it as a simpler problem, or one that is similar and already solved. We discuss those opportunities here.

      • Try It Now Book

        Work these exercises to see how well you understand this material.

    • 5.4: Conditional Probability and Independent Events

      • Conditional Probability Page

        Events can be dependent or independent of something else. This video considers events whose probability of occurrence is independent of all other events.

      • Independent Events Page

        Read this section.

      • Try It Now Book
        Work these exercises to see how well you understand this material.

    • Unit 5 Assessment

      • Unit 5 Assessment Quiz
        Receive a grade

        Take this assessment to see how well you understood this unit.

        • This assessment does not count towards your grade. It is just for practice!
        • You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
        • You can take this assessment as many times as you want, whenever you want.