Probability & Statistics

Factorials, arrangements of all or some objects, repeated letters, and seating with restrictions.

Choosing without order: nCr, committees, at-least and at-most counts, and when order matters vs when it doesn't.

The triangle that counts everything: binomial coefficients, expanding powers, and finding specific terms.

Sample spaces, events, equally-likely outcomes, complements, and the addition rule with Venn diagrams.

How information changes chance: P(A|B), the multiplication rule, independence, weighted trees, and Bayes by table.

Turning outcomes into numbers: probability distributions, expected value, variance, and what makes a game fair.

Repeated independent trials: binomial probabilities, expected count np, shape, and simulation.

Center and spread done right: mean, median, IQR, standard deviation, boxplots, and the 1.5×IQR outlier fence.

Histograms and shape, percentiles, z-scores, and the normal curve with the 68–95–99.7 rule.

Scatterplots, the correlation coefficient, the least-squares line, and why correlation is not causation.

Random sampling, bias, experiments vs observation, simulation-based inference, and margin of error — the capstone.