Probability
Lessons in this chapter
About Probability
Probability closes the course with a full set of tools for calculating the likelihood of both simple and combined events.
Introduction to Probability and Geometric Probability cover the basic definition of probability and its geometric version, where probability is calculated using area or length ratios instead of counting outcomes.
Certain Events and Complement of an Event and Probability of Union of Events (‘OR’ Events) cover the extremes (certainty and impossibility) and how to combine the probabilities of two events joined by ‘or,’ while Exhaustive Events and Fundamental Principle of Counting build the counting techniques needed to find a total number of outcomes in more complex situations.
Probability of 'AND' Events and Conditional Probability close the main content by combining two events with 'and,' including cases where one event's probability depends on another already having happened, and Two-Way Tables and Probability applies every probability rule to data organized in a two-way table.
This is the longest chapter in the course at nine lessons, and each one opens as a Geometry worksheet in the page, including Geometric Probability, Fundamental Principle of Counting and Two-Way Tables and Probability. Every question is scored as you answer it, so using the plain multiplication rule on events that are actually dependent is flagged while the problem is still in front of you. The worksheets are free to try, with no login needed for your first 3.
Frequently asked questions
Introduction to Probability and Geometric Probability start with likelihood as a ratio, first by counting equally likely outcomes and then by comparing lengths or areas. Certain Events and Complement of an Event, Probability of Union of Events (OR Events) and Exhaustive Events build the addition rules, Fundamental Principle of Counting counts combined outcomes without listing them, and Probability of AND Events, Conditional Probability and Two-Way Tables and Probability handle events that depend on each other. The chapter sits in the high school Statistics and Probability conceptual category (S), with the geometric probability lesson borrowing length and area ideas from Geometry (G).
Geometric probability calculates likelihood using a ratio of areas or lengths (like the probability a randomly thrown dart lands in a specific region) instead of counting a finite number of equally likely outcomes.
The complement of an event is everything that ISN'T that event, and its probability is always 1 minus the original event's probability, since the event and its complement together cover every possible outcome.
Add the two events’ individual probabilities, then subtract the probability of both happening at once (to avoid double-counting any overlap). This is the general addition rule for "or" probabilities.
A set of events is exhaustive if, together, they cover every single possible outcome, at least one of them is guaranteed to happen.
It states that if one event can happen in m ways and a second independent event can happen in n ways, the two together can happen in m × n ways: the basic tool for counting combined outcomes without listing every single one.