Probability Visual Tools

Compare probability distributions side-by-side with interactive visualization tools. Switch between discrete and continuous distributions to understand their unique properties, parameters, and real-world applications.

Interactive coin toss simulators demonstrate probability through repeated trials. Run probability simulations, analyze sample spaces, and watch the Law of Large Numbers emerge with real-time coin flip statistics.

Calculate dice probabilities with interactive simulators and sample space explorers. Roll single or multiple dice, visualize sum distributions, and explore all possible outcomes with statistical analysis.

Interactive Venn diagrams reveal relationships between probability events. Understand intersections, unions, and complements through dynamic 2-set and 3-set configurations with real-time probability calculations.

Explore conditional probability through tree diagrams, Venn diagrams, waffle charts, and contingency tables. See how P(A|B) changes with different visualization methods and interactive examples.

Learn expected value through interactive visualizations. See how probability weights combine with outcomes to determine long-run averages.

Interactive tool for understanding variance through visual exploration. Drag data points to see real-time variance calculations, toggle between population and sample variance, and watch step-by-step breakdowns of how variance measures data spread.

Interactive visualizers demonstrate Markov's and Chebyshev's inequalities with dynamic probability bound calculations. Adjust parameters to see how these fundamental theorems provide tail probability estimates across different distributions.

Visualize probability functions with interactive visualizers for both discrete and continuous distributions. Adjust parameters in real-time to see how PMF and PDF curves change for Binomial, Poisson, Normal, Exponential, and other distributions.

Understand cumulative distribution functions through interactive charts for discrete (Binomial, Poisson, Geometric) and continuous distributions (Normal, Exponential, Uniform). Adjust parameters to see how probability accumulates across different distributions with real-time CDF visualizations.

Calculate marginal probabilities using the law of total probability with an interactive tree diagram. The tool shows how probabilities flow through partitioned sample spaces, displaying joint probabilities, conditional probabilities, and Bayes' theorem calculations in real-time.