DV Math Resource Library - High School and Early College Probability

Probability is a part of many high school and early college math courses, but students often struggle with this area of mathematics.

Part of the problem is that probability is a large area with many topics, but students are often learning just a few of these topics in any one course which makes it difficult to see how what they are learning fits into the 'big picture'.

I created this video series to help students get help on individual probability topics, but also to allow students to see this larger picture of probability.

Each topic has one or more 'concept' videos which explain a small set of topics with emphasis on understanding why in addition to how these strategies work, followed by an 'examples' video which you can use to practice: pause the video, try the problem, then unpause and see if your solution was correct!

You can pick individual videos to watch, but later videos do assume you have the knowledge from the previous videos.

I look forward to sharing the details of this fascinating area of mathematics with you!
-- Mr. Felling

Lesson 1: Introduction: What is Probability? Terminology and Notation

Lesson 1 Concept: Probability Terminology and Notation

Used in: Algebra 1, Algebra 2, Honors algebra 2, Precalculus, Honors Finite Math/Brief Calculus, AP Statistics

Lesson 2: Probability with equally-likely outcomes

The structure for finding probability with equally-likely outcomes is the simplest of all, but these can be some of the most difficult probability problems because there are so many ways to count!

Lesson 2a Concept: Review of Counting Strategies
Lesson 2b Concept: Probability with Equally-Likely Outcomes
(Lesson 2 Examples/Practice)

Used in: Algebra 1, Algebra 2, Honors Algebra 2, Precalculus, Honors Finite Math/Brief Calculus, AP Statistics

Lesson 3: Conditional Probability

Sometimes, we find probability given a condition. In that case, we are restricted to only a portion of the sample space: the conditional sample space.

Lesson 3 Concept: Conditional Probability
(Lesson 3 Examples/Practice)

Used in: Algebra 2, Honors Algebra 2, Precalculus, Honors Finite Math/Brief Calculus, AP Statistics

Lesson 4: Compound Event Probability (OR cases)
and Disjoint (Mutually-Exclusive) Events

When one event OR another event can happen to be 'successful' we ADD the probabilities...but there is a catch: we must substract the overlap. There is a special case which simplies the formula: disjoint (also known as mutually-exclusive) events.

Lesson 4 Concept: Compound Event Probability (OR cases), Disjoint (mutually-exclusive) Events
(Lesson 4 Examples/Practice)

Used in: Algebra 2, Honors algebra 2, Precalculus, Honors Finite Math/Brief Calculus, AP Statistics

Lesson 5: Compound Event Probability (AND cases)
and Independent Events

When one event AND another event can happen to be 'successful' we MULTIPLY the probabilities...but there is a catch: one probability must be a conditional probability. There is a special case which simplies the formula: independent events.

Lesson 5a Concept: Compound Event Probability (AND cases)
Lesson 5b Concept: Independent Events
(Lesson 5 Examples/Practice)

Used in: Algebra 2, Honors Algebra 2, Precalculus, Honors Finite Math/Brief Calculus, AP Statistics

Lesson 6: Using AND and OR formulas together,
Using Tree diagrams for conditional probability, and Baye's Formula

Using AND and OR formulas together is a powerful technique for solving problems. Bayes' Formula (reverse conditional probability) problems are best solved using a tree diagram.

Lesson 6 Concept: AND/OR formulas used together, tree diagrams and Baye's Formula problems
(Lesson 6 Examples/Practice)

Used in: Honors algebra 2, Precalculus, Honors Finite Math/Brief Calculus, AP Statistics

Lesson 7: Using Venn diagrams, Subsets

Using a Venn diagram is a great strategy for word problems with a large amount of information and is the best strategy for analyzing subsets.

Lesson 7 Concept: Venn Diagrams and Subsets
(Lesson 7 Examples/Practice)

Used in: Honors Algebra 2, Precalculus, Honors Finite Math/Brief Calculus, AP Statistics

Lesson 8: Discrete Probability Models

There are certain situations which occur so frequently that we have standardized ways to compute the probability called probability models. For discrete problems (involving 'counts') we can use the Binomial, Geometric, or Poisson models (each is used in a different situation).

Lesson 8a Concept: The Binomial Model
Lesson 8b Concept: The Geometric, and Poisson Models, Comparison of models
Lesson 8c Concept: Discrete Probability Model Distributions and Expected Value
(Lesson 8 Examples/Practice)

Used in: Honors Finite Math/Brief Calculus, AP Statistics

Lesson 9: Continuous Probability Models

We need different strategies for handling cases where there is an infinite number of possible outcomes because the variable is continuous. The most common continuous model, the Normal curve, is used is many math courses and is covered in the next lesson, but here we explore the foundational concepts about how continuous probability models work, add define expected value and average value for these models.

Lesson 9a Concept: Continuous vs. Discrete Probability
Lesson 9b Concept: Continuous Models, Expected and Average Value for Continuous Models
(Lesson 9 Examples/Practice)

Used in: Honors Finite Math/Brief Calculus

Lesson 10: The Normal Probability Model

Many naturally occurring phenomena vary around a typical value according to a specific distribution: the Normal distribution. Here, we explore this powerful probability model and learn how it can sometimes be used to approximate a Binomial model.

Lesson 10a Concept: The Normal (Gaussian, bell-curve) Model
Lesson 10b Concept: Using a Normal model to approximate a Binomial model
(Lesson 10 Examples/Practice)

Used in: Algebra 2, Honors Algebra 2, Precalculus, Honors Finite Math/Brief Calculus, AP Statistics

Lesson 11: Combining / Transforming Multiple Continuous Distributions

For some continuous probability problems, we can use standard continuous models but need to transform a single distribution or combine multiple distributions.

Lesson 11 Concept: Transforming and Combining Distributions
(Lesson 11 Examples/Practice)

Used in: AP Statistics

Lesson 12: Putting it all together

How do we know which of the many strategies we have for probability we should use to solve a particular problem? It takes much practice, but we can use a strategy tree to help as we are practicing.
Note: These are very long videos, because they include discussion about how to select a strategy and often show multiple ways to solve. Since these are videos, you can scan around in them to focus on just the problems you want to see. Suggest that you print out the Probability Strategy Tree PDF below to use while solving.