Probability is the mathematical language we use to describe uncertainty. In engineering, almost nothing is known with perfect certainty: material strengths vary, sensors drift, components fail at unpredictable times, and measurements carry error. Probability gives us a disciplined way to quantify that uncertainty on a fixed scale from 0 (impossible) to 1 (certain), so that vague statements like "this part will probably hold" can be replaced by numbers that support design decisions and risk analysis.
This week you are building the vocabulary that the rest of the course depends on. Terms such as experiment, outcome, sample space, and event have precise technical meanings, and the rules you will learn later (complement, addition, multiplication) are stated in that vocabulary. You will also meet the distinction between theoretical probability, derived from the structure of the experiment, and experimental (empirical) probability, estimated from observed data — a distinction that matters any time you compare a model to real test results.
As you watch the videos below, keep a running glossary. Note how each presenter defines the sample space and how they list or diagram outcomes, watch for how probabilities are interpreted in words rather than just computed, and pay attention to any discussion of relative frequency and what happens as the number of trials grows. Where the videos overlap, compare notation; where they differ in emphasis, ask yourself which framing is most useful for an engineering problem.
A crash course that works through the core definitions of probability, including sample spaces and the events defined within them, along with the mathematical notation used to express them. At roughly nineteen minutes it is the most detailed of the three and is likely to cover basic rules and worked examples rather than stopping at definitions. Treat it as your main reference pass through the terminology.
Its stated focus on key definitions, sample spaces and events maps directly onto the Key Probability Terminology subtopic, and its length allows the precision that a foundations lecture requires.
A brief, accessible introduction framed around the idea that we cannot know the outcome of a situation until it happens, which leads naturally into why we quantify likelihood at all. Expect plain-language explanations of what a probability value means and simple everyday examples rather than heavy notation. It is a good first watch or a quick refresher before the longer video.
Data Science Dojo pitches content at practitioners, so the framing around uncertainty and interpretation fits the Uncertainty and Its Role in Probability and Probability in Data Analysis subtopics well.
An opening lesson from a Wolfram U course that answers the question "what is probability?" before the course moves on to random variables and common distributions. It should establish the probability scale and the basic concepts in a compact, carefully structured way. Think of it as a clean definitional anchor for the topic.
It comes from a reputable technical publisher and, as the first lesson of a structured course, it gives the concise and accurate definitional statement that the What Is Probability? and The Probability Scale subtopics call for.
Together these videos build the foundation the module outcomes rest on. The emphasis on sample spaces and events supports MO1, since you cannot construct a sample space systematically without first knowing precisely what one is. The definitional and notational work prepares you for the complement, addition and multiplication rules in MO2 and for choosing among them in MO5. The treatment of uncertainty and of what a probability value actually means supports MO4's requirement to interpret results in plain engineering language, while the contrast between probabilities derived from structure and those estimated from observed outcomes sets up the theoretical versus experimental comparison and the Law of Large Numbers discussion in MO3.
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.
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.
Probability can be approached from two directions. Theoretical probability is what you reason out in advance: if a process has equally likely outcomes, you count the outcomes favorable to an event and divide by the total number in the sample space. Experimental (or empirical) probability is what you measure: you run or observe trials and divide the number of times the event actually occurred by the number of trials performed. Both produce a number between 0 and 1, but they are obtained in fundamentally different ways and they carry different assumptions.
This distinction matters in engineering because many real systems do not come with a tidy list of equally likely outcomes. You rarely know the true failure probability of a component from first principles, so you estimate it from test data or field observations. Conversely, when a model is available, theoretical probability lets you predict behavior before building anything. The bridge between the two is the Law of Large Numbers, which says that as the number of independent trials grows, the relative frequency of an event tends to settle near its true probability. That is why a short run of 10 coin flips can look lopsided while 10,000 flips look nearly even.
As you watch, keep three questions in mind. First, how is each probability computed — by counting outcomes in a sample space, or by counting occurrences in data? Second, what does the Law of Large Numbers actually promise, and what does it not promise (it does not say that a run of bad luck must be "balanced out")? Third, when experimental results disagree with theoretical predictions, what are the plausible explanations: too few trials, a biased or unfair process, or a flawed model assumption? Being able to argue which explanation applies is a core engineering skill.
A short, direct introduction that defines experimental and theoretical probability side by side and walks through how to compute each. Based on its title and description, it focuses on the contrast between the two approaches and shows worked examples of calculating probabilities both ways. Expect simple, familiar settings such as dice, coins, or spinners used to make the comparison concrete.
At roughly four minutes it is the most efficient entry point for the first three subtopics — defining each type of probability and naming the key differences — and gives you shared vocabulary before the longer, more mathematical treatments.
Steve Brunton presents the Law of Large Numbers as a formal result in probability, framing it as a stepping stone toward broader results such as the Central Limit Theorem. The video is likely to cover what convergence of a sample average means, why repeated independent trials drive the observed frequency toward the true probability, and the conditions under which the result holds. Expect a mix of intuition and mathematical statement rather than arithmetic drills.
Brunton is a mechanical engineering professor known for clear, engineering-oriented treatments of applied mathematics, making this a strong fit for the Law of Large Numbers subtopic at the level expected in an engineering probability course.
A lecture segment from a data science course that explains the Law of Large Numbers in the context of working with data and simulations. It is likely to show how an empirical estimate behaves as the number of observations increases, illustrating convergence through computation rather than proof. The framing emphasizes practical use of sampled data.
It complements the more theoretical treatment by showing the data-driven side of the same idea, supporting the subtopics on practical applications and on comparing experimental results against theoretical values.
Together these videos target MO3 most directly: the first clarifies the definitions and derivation methods of theoretical versus experimental probability, while the two Law of Large Numbers videos explain the principle that links an observed relative frequency to an underlying theoretical probability. Computing theoretical probability requires enumerating outcomes, so the examples reinforce the sample-space thinking in MO1 and the basic rule application in MO2 and MO5. The data-oriented treatment of convergence also supports MO4 by showing how a probability estimate drawn from trials should be stated and interpreted — including how much confidence a given number of trials actually warrants in a real decision-making setting.
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.
Probability rules are the grammar of uncertainty. Once you can describe a sample space, you need a reliable set of operations for combining events: what happens when you want the chance that an event does not occur, the chance that at least one of two events occurs, or the chance that two events both occur. The core rules — complementary probability, the addition rule (for mutually exclusive events and the general form that subtracts the overlap), the multiplication rule (for independent events and the general form that uses a conditional probability), and conditional probability itself — cover nearly every basic computation you will do this semester.
In engineering, these rules show up constantly: the probability a redundant system fails only if every component fails, the probability a part is out of tolerance on at least one dimension, the probability a test flags a defect given that the part is actually defective. Getting the right answer usually depends less on arithmetic than on correctly identifying which rule applies and whether the events overlap or influence each other.
As you watch the videos below, keep three questions in mind. First, are the events mutually exclusive (can they happen together)? Second, are they independent (does knowing one occurred change the probability of the other)? Third, when a problem has several steps, which rule applies at each step and how do the pieces combine? Try to pause each video before the solution is shown and set up the calculation yourself.
A full lesson on the multiplication rule and conditional probability, framed around a real data question about identifying honest online dating profiles. Based on the title and accompanying handout, it should develop conditional probability notation, the general multiplication rule, and the connection between independence and the simpler product form, all within an applied context.
Skew The Script is known for statistically careful lessons built on real data, and this video covers the general multiplication rule and conditional probability — the hardest subtopics here — while modeling how to interpret results in plain language.
A short worked example applying the addition rule for probability, covering both the mutually exclusive case and the non-mutually exclusive case. The description indicates it contrasts the two situations, so you should see where the 'minus the intersection' term comes from and when it drops out.
It directly targets two of the subtopics — the simple addition rule and the general addition rule — in a compact, example-driven format that makes the overlap correction concrete rather than abstract.
A brief example-based walkthrough of the multiplication rule for probability. Expect a problem set up so that the probability of a joint event is found by multiplying individual probabilities, with attention to the conditions that make that multiplication valid.
It pairs naturally with the addition rule video from the same producer, giving you a consistent treatment of the 'and' rule alongside the 'or' rule so the distinction between them stays clear.
Together these three videos give direct practice with the computational core of the module. The addition and multiplication rule examples support MO2 by showing the rules applied to concrete problems, and the contrast between mutually exclusive and overlapping events, and between independent and dependent events, builds the judgment needed for MO5 when you must choose a rule in a multi-step problem. The conditional probability lesson extends this to the general multiplication rule and, because it works from a real-world scenario, supports MO4 by modeling how to state what a probability actually means in context. Note that the videos focus on the rules themselves, so you should rely on the module readings and class materials for constructing sample spaces (MO1) and for the theoretical versus experimental probability distinction and the Law of Large Numbers (MO3).
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.
A probability is a number, but a number by itself rarely helps anyone make a decision. This topic is about the step that comes after the arithmetic: saying clearly what a probability of 0.03, 0.5, or 0.97 actually means for the situation in front of you. That includes describing likelihood in plain language, explaining what the complement tells you, and being careful about whether a value came from theory (counting equally likely outcomes in a sample space) or from experiment (observing relative frequencies over many trials).
This matters in EGN3443 because engineers are usually not the final decision-maker acting alone. You will report reliability estimates, failure chances, and test results to managers, clients, regulators, and the public. A well-calculated probability that is poorly communicated — or that is quietly conditional on something the audience does not know about — can lead to a bad decision just as easily as a wrong calculation.
As you watch the videos below, pay attention to three things. First, how each presenter moves from a formula or a diagram back to a sentence about the real situation. Second, how sample spaces and the basic rules (complement, addition, multiplication) are used to justify a claim about fairness or risk. Third, where joint and conditional probabilities show up, and how the wording changes when you condition on information you already have.
A short overview of the core probability rules, presented through real-world framing and Venn diagrams. Based on its title and description, it covers how the rules fit together — including unions, overlaps, and complements — and uses decision-making scenarios as the motivating context. The Venn diagram approach gives a visual way to see why the addition rule needs to correct for double counting.
Study Hall is a PBS/Crash Course production aimed at general college audiences, so the explanations stay in plain language rather than heavy notation — a good match for the translating-probability-into-words and complementary-probability subtopics.
Khan Academy works through an example of judging whether a procedure is fair by examining the probabilities involved. The focus is on checking whether each party or outcome has an equal chance, which requires laying out the possible outcomes and comparing their likelihoods. It is a compact, worked example rather than a lecture on theory.
This is a direct demonstration of applying probability to inform a judgment about a real situation, and it shows how grounding your interpretation in the full set of outcomes is what makes the conclusion defensible.
Primer builds up the binomial distribution slowly, using animation and simulated trials rather than starting from the formula. Expect a careful look at how repeated independent trials generate a distribution of outcomes, and how counting arrangements of successes and failures connects to the multiplication and addition rules. Because the video runs simulations, it also illustrates how observed frequencies behave relative to theoretical values.
It is the clearest video here for seeing the theoretical-versus-experimental distinction in action, and its visual counting of outcome sequences reinforces how sample spaces underpin any probability you later interpret.
Together these videos reinforce the module outcomes from the interpretation side. The Study Hall episode and the Primer video both make the structure of a sample space visible — through Venn diagrams and through enumerated sequences of trials — supporting MO1, while their treatment of unions, complements, and repeated independent events supports MO2 and MO5 by showing when each rule applies. Primer's simulations give a concrete feel for how experimental frequencies relate to theoretical values and the Law of Large Numbers (MO3). The Khan Academy fairness example and the decision-oriented framing in Study Hall model MO4 most directly: each ends not with a number but with a plain-language statement about what that number means for the choice being made.
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.