Pick a lesson — or pick up where you left off.
Six bite-size lessons, one per objective. Most students do them in order, but you can jump around if you want a refresher on a specific idea.
Start Lesson 01Simple probability.
Compute the probability of a simple event as the ratio of favorable outcomes to total outcomes, and express the answer as a fraction in lowest terms.
Open lessonThe fundamental counting principle.
Apply the fundamental counting principle to find the number of possible outcomes for a multi-step procedure by multiplying the number of choices at each step.
Open lessonSample spaces and the addition rule.
Build a sample space for a single experiment and compute P(A or B) using the addition rule, including the correction for overlap when events are not mutually exclusive.
Open lessonPermutations and combinations.
Distinguish between permutations (order matters) and combinations (order doesn't), and apply the P(n, r) and C(n, r) formulas to standard selection problems.
Open lessonExpected value.
Compute the expected value of a discrete random variable as the sum of value × probability across all outcomes, and interpret the result as the long-run average per trial.
Open lessonTheoretical vs experimental probability.
Compute both theoretical and experimental probability for compound independent events, compare the two, and describe how they converge as the number of trials increases (the Law of Large Numbers).
Open lesson