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Learn Probability

Reason clearly about chance, risk and uncertainty.

Free to start. Built from a single prompt. No credit card.

Probability is the mathematics of uncertainty. It starts with sample spaces, events and counting, then builds the tools that matter most in practice: conditional probability, independence, Bayes' theorem, random variables, expected value and variance. From there you meet the named distributions, such as binomial, geometric, Poisson, uniform, exponential and normal, and the big limit results, the law of large numbers and the central limit theorem. Probability is also full of famous intuition traps like the Monty Hall problem and the birthday problem. Learnr builds a personalized probability course and teaches it in short interactive lessons with simulations and worked puzzles.

How to learn Probability, step by step

Learn to define the sample space. For every problem, write down the possible outcomes and check whether they are equally likely. Many wrong answers to dice, card and coin problems come from an unclear or unequal sample space.
Master counting and complements. Use permutations and combinations to count outcomes, and compute "at least one" probabilities as one minus the probability of none. The birthday problem is a good exercise in both.
Get conditional probability and Bayes right. Use tree diagrams and two-way tables to compute P(A given B), then apply Bayes' theorem to classic medical test problems. Notice how a rare condition with an accurate test can still produce mostly false positives.
Work with random variables and expectation. Compute expected value and variance, and use linearity of expectation, which works even when variables are dependent. Problems like the expected number of fixed points in a random shuffle show its power.
Learn the key distributions by their stories. Connect binomial to counts of successes, geometric to waiting for the first success, Poisson to rare events in an interval and exponential to waiting times. Short Learnr lessons each day help these stories and formulas stick together.
Simulate to check your intuition. Write a few lines of Python or use a spreadsheet to simulate Monty Hall, coin streaks or sample means, and compare results with your calculations. Simulation also makes the central limit theorem visible.

What you'll learn

Compute probabilities with counting, complements and the addition rule
Use conditional probability, independence and Bayes' theorem correctly
Work with random variables, expected value, variance and linearity of expectation
Recognize and apply common discrete and continuous distributions
Explain the law of large numbers and the central limit theorem

What's inside your Probability course

A sample path Learnr builds for Probability. Your real course adapts to your goal and level.

1. Sample spaces, events and counting
2. Conditional probability and independence
3. Bayes' theorem and reasoning with evidence
4. Discrete random variables and expectation
5. Continuous distributions and the normal curve
6. Joint distributions and limit theorems

How long does it take to learn Probability?

An introductory probability course takes about 2 to 4 months at 4 to 6 hours a week. A calculus-based course with continuous and joint distributions, like a typical university probability class, usually takes 3 to 5 months and benefits from strong calculus.

What you need before you start

Algebra and comfort with fractions. Basic counting helps. Calculus is needed only for continuous distributions in a university-level course, and a non-calculus introduction covers the discrete core.

Common mistakes to avoid

Assuming events are independent without checking, such as multiplying probabilities for draws made without replacement.
Confusing P(A given B) with P(B given A), the classic error behind misreading medical test results.
Believing in the gambler's fallacy, that a coin is "due" for heads after several tails. Independent trials have no memory.

How Learnr builds your course

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Probability questions, answered

Should I learn probability or statistics first?

Probability first is the traditional order, since statistics uses probability to measure uncertainty in estimates. Many introductory statistics courses teach just enough probability along the way, so either path works for applied goals.

Why is the Monty Hall problem so confusing?

Because the host's choice carries information. He always opens a door without the car, so switching wins whenever your first pick was wrong, which happens two times out of three. Simulating it is the fastest way to be convinced.