← All ArticlesProbability

Probability

Basic probability rules, conditional probability, Bayes' theorem, expected value, and the counting methods that underpin every branch of inferential statistics.

14 articles

Illustration: Any distribution keeps at least 75% within 2σ of its mean; this skewed one keeps 96%

Sep 28, 20267 min read

Chebyshev's Inequality: A Distribution-Free Bound on Spread

Read article →

Illustration: Multiply along the branches to get each joint probability; the four leaves sum to 1

Sep 26, 20268 min read

Probability Trees: How to Build and Read Them, With Worked Examples

Read article →

Illustration: Add the singles, subtract the pairs, add back the triple — nothing is counted twice

Sep 22, 20268 min read

The Inclusion–Exclusion Principle: Counting and Probability for Overlapping Events

Read article →

Illustration: Expectations add — even when the two quantities are dependent

Sep 21, 20268 min read

Linearity of Expectation: The Shortcut for Adding Averages

Read article →

Illustration: The running proportion of heads wanders early, then settles inside a shrinking ±1.96/(2√n) band

Sep 20, 20267 min read

The Law of Large Numbers: Why Sample Averages Converge on the Truth

Read article →

Illustration: Joint probabilities fill the table; the margins (amber) are their row and column sums

Sep 15, 20268 min read

Joint, Marginal, and Conditional Probability: Reading a Two-Way Table

Read article →

Illustration: The ROC curve traces the trade-off between catching cases and false alarms at every threshold

Sep 10, 20268 min read

Sensitivity, Specificity, and ROC Curves: Measuring How Good a Test Really Is

Read article →

Illustration: Choosing 3 of 3 letters gives 6 ordered arrangements but only 1 unordered group

Sep 8, 20267 min read

Permutations and Combinations: When Order Matters, and When It Doesn't

Read article →

Illustration: The expected value is the balance point of the distribution — a long-run average, not a forecast

Sep 3, 20267 min read

Expected Value: The Long-Run Average, Explained With Worked Examples

Read article →

Illustration: Switching wins whenever your first pick was wrong — which is two times out of three

Aug 18, 20267 min read

The Monty Hall Problem: Why Switching Doors Really Does Double Your Odds

Read article →

Illustration: Probability is capped at 1; odds run to infinity: p = 0.5 is 1:1, p = 0.9 is 9:1

Aug 14, 20266 min read

Odds vs. Probability: What's the Actual Difference?

Read article →

Illustration: Of 100 people, 1 has the condition and 9 healthy people also test positive: a positive means 10%

Aug 13, 20268 min read

Bayes' Theorem: The Formula, the Medical Testing Example, and Why Base Rates Matter

Read article →

Illustration: The addition rule: subtract the overlap, or it gets counted twice

Aug 11, 20268 min read

Basic Probability Rules: Addition, Multiplication, and Conditional Probability

Read article →

Aug 6, 20267 min read

The Birthday Problem: Why 23 People Is Enough for a 50/50 Shared Birthday

Read article →

Browse other topics

Descriptive Statistics

Mean, median, mode, standard deviation, variance, quartiles and the interquartil…

Distributions

The normal distribution, binomial distribution, t-distribution, z-scores, and th…

Sampling & Inference

Sampling distributions, the Central Limit Theorem, standard error and confidence…

Hypothesis Testing

Null and alternative hypotheses, p-values, Type I/II errors, t-tests, chi-square…

Regression & Correlation

Pearson correlation, simple and multiple linear regression, R², and residual ana…

Data Science & Applications

Exploratory data analysis, data visualization, A/B testing, and Bayesian statist…

Never miss a Probability article

Get new statistics articles, study tips, and platform updates delivered to your inbox every Thursday.