Introduction to Probability Lab
Probability for business and analytics, from the first rules to confidence intervals: theory, live charts you can move, and the code an analyst would write.
Chapters
The course in 11 chapters, from events and Bayes' rule to the central limit theorem and confidence intervals. Start with chapter 1 and work through in order, or open any chapter on its own.
Sample spaces and events, the complement and addition rules, and the law of large numbers.
Conditional probability, independence, tree diagrams and Bayes' rule with base rates.
PMF, PDF, CDF and percentiles; expected value, variance and standard deviation.
Discrete and continuous: when "all equally likely" is a fair model, and when it is not.
The four conditions, the formula, its mean and variance, and the off-by-one trap.
Counts in an interval, the rate λ, and the Poisson as the limit of the binomial.
Measurements, not counts: density against probability, areas and percentiles.
Standardising, the 68-95-99.7 rule and the normal approximation to the binomial.
Waiting times, memorylessness and the link to the Poisson.
The standard error, the central limit theorem, and what it does not promise.
Point estimates, the t distribution, z and t intervals, and how to read them.
Playgrounds, simulations and a drill that go with the chapters, and exercises checked as you answer.
A Venn diagram and a tree for two events, each rule read term by term, and Bayes' rule with 10,000 people.
Flip a coin or roll a die, one at a time and then in bursts, and watch the relative frequency settle.
A drill that turns sentences into inequalities, scipy calls and Excel formulas, without the off-by-one trap.
Balls bounce left or right through rows of pegs and pile up into the binomial distribution.
Fit a distribution to the lab's datasets: a histogram with the fitted curve, a Q-Q plot, summary statistics and the tails.
Compare values measured in different units on one scale, and see the rule's three bands shaded on the normal.
Watch n step up from 5 to 200 as the binomial's bars thin into the normal curve, with and without the continuity correction.
Draw samples from four populations and watch their means pile up into the normal curve the central limit theorem predicts.
Build z and t intervals, then draw 100 samples and count how many of their intervals contain the true mean.
50 exercises across the eleven chapters, with hints one at a time and worked solutions.
A vaccine batch, a share's returns, a bookshop, a software team and a bulb supplier, each worked through step by step with checked answers.
Check a new batch of a vaccine: unsatisfactory doses among 10 and 20 as binomials, then the time a dose takes to work as a normal.
Model a share's returns with the normal: a day, a year by the square root of time, and the fat tails the model misses.
A year of daily book sales as a discrete uniform, the boundaries stated exactly, and a month's average by the central limit theorem.
Model how long a bug takes to fix, set aside a model that looks plausible and is not, and budget a sprint with the central limit theorem.
A supplier claims 5 % of its bulbs are faulty, and a test finds 4 in 20: binomial tails as the first step towards a hypothesis test.
Reference
For looking things up and for teaching: every term with a link to where it is explained, every distribution and rule with its code, and lecture paths with speaker notes.
90 terms from the chapters and tools, each linked to the section that explains it.
Every distribution and rule on one printable page: the formula, when to use it, and the scipy and Excel that compute it.
3 guided routes through chapters, tools and case studies for a teaching session, with speaker notes at every step.
Put any of the eight explorers on your own site, blog or course page with one line of HTML.
Explorers
Calculators with sliders and typed inputs, one for every distribution in the course, whose charts change as you move them. Ask a question and see which bars or which area it counts.
Every whole number from a to b equally likely: a fair die, or a bookshop's daily sales.
Any value between a and b equally likely: a probability is a length divided by the width.
Successes in n independent trials, each with probability p: move n and p and watch the bars.
Counts of events in an interval at an average rate λ: calls per hour, defects per batch.
Measurements around a mean μ with spread σ: a probability is an area under the bell.
Waiting times between events at rate λ: memoryless, with a long right tail.
The normal's heavier-tailed cousin, for a mean judged from a small sample.
The sum of k squared standard normals: the building block of Student's t.