Every probability problem starts with the same question: what could happen? The sample space is the complete list of possible outcomes of an experiment, and an event is any subset of that list — the outcomes we actually care about. Before you can assign a number to "the probability that a sampled part is defective" or "the probability that at least one of three sensors fails," you have to be able to write down the outcomes clearly and without gaps or overlaps.
In this course, sample spaces and events are the structural foundation for everything that follows: counting rules, the addition and multiplication rules, conditional probability, and eventually random variables and distributions. Most errors in probability problems are not arithmetic errors — they come from a poorly defined sample space, from double-counting outcomes, or from assuming outcomes are equally likely when they are not. Learning to build sample spaces systematically, using lists, tables, and tree diagrams, protects you from those mistakes.
As you watch the videos below, pay attention to three things. First, notice how each presenter decides what counts as a single outcome (an ordered pair? an unordered set? a sequence?), because that choice determines the whole sample space. Second, track the set language — union, intersection, complement, and disjoint (mutually exclusive) events — and how it maps onto plain-English phrases like "and," "or," and "not." Third, watch for when the equally likely assumption is used to compute a probability as a ratio of counts, and ask yourself whether that assumption would hold in an engineering setting.
This Wolfram U video defines the sample space and events for a probability experiment and then works through calculations based on those definitions. Based on its description, it also visualizes core set-theory operations — union, intersection, and complement — using worked examples. Expect a mix of formal definitions and graphical illustrations of how events relate to one another inside a sample space.
It directly covers defining a sample space, defining an event, and the relationships between events, and the visual treatment of set operations makes the connection between "and/or/not" language and probability notation concrete.
A short, focused screencast from LearnChemE (faculty at the University of Colorado Boulder) introducing sample spaces and events. In about five minutes it is likely to state the definitions and illustrate them with a compact worked example, in the style of the engineering-oriented LearnChemE screencast library.
It is produced by engineering faculty for engineering students, so the framing matches this course, and its brevity makes it an efficient first pass or a quick review before attempting problems.
This longer crash course walks through the key definitions and mathematical foundations of probability, including sample spaces and their events. Its description indicates it builds from basic terminology toward the broader set of probability concepts, so expect notation, vocabulary, and the logic connecting outcomes, events, and probability assignments.
At roughly nineteen minutes it gives the most complete treatment of the three, situating sample spaces and events within the wider probability framework you will use for the rest of the module.
Together these videos build the vocabulary and habits that MO1 requires: identifying outcomes precisely and organizing them into a complete sample space using lists, tables, or tree diagrams. The set-theory content — union, intersection, complement, and mutually exclusive events — is the direct groundwork for the complementary, addition, and multiplication rules in MO2 and for choosing among them in MO5. Understanding when outcomes are equally likely also clarifies how theoretical probabilities are derived, supporting the comparison with experimental probability in MO3, and defining events in plain language before computing them is exactly the translation skill you need to interpret a probability value in an engineering context for MO4.
These videos were chosen from YouTube on October 2, 2026. Each has captions; the player turns them on. Videos on YouTube can be changed or removed — if one no longer plays, tell your instructor. If a player does not appear, use its Watch on YouTube link.