Probability Calculator
Simulate coin flips, dice rolls, generate random numbers, calculate combinations and permutations, and explore probability distributions with visual trees. All calculations happen locally — nothing leaves your browser.
How to Use the Probability Calculator
- Choose a tab — select coin flip, dice roll, random numbers, combinations, binomial, normal distribution, or probability tree.
- Set parameters — enter the number of trials, probabilities, or values as needed.
- Click Calculate/Generate — see results instantly with visual distributions.
- Explore distributions — view bar charts for binomial and probability trees for visual learning.
Understanding Probability
Probability quantifies the likelihood of events, ranging from 0 (impossible) to 1 (certain). It's the foundation of statistics, gambling, risk assessment, and scientific research.
This calculator helps you understand core probability concepts through hands-on simulation. Flipping coins and rolling dice thousands of times reveals the law of large numbers — as trials increase, observed frequencies converge to theoretical probabilities.
Frequently Asked Questions
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. It's defined by two parameters: n (number of trials) and p (probability of success). For example, getting exactly 5 heads in 10 coin flips follows Binomial(n=10, p=0.5).
A z-score tells you how many standard deviations a value is from the mean. A z-score of 2 means the value is 2 standard deviations above the mean. It's used to compare values from different distributions and to calculate probabilities using the standard normal table.
Combinations (nCr) count selections where order doesn't matter — choosing 3 topping from 10. Permutations (nPr) count selections where order matters — choosing a president, VP, and treasurer from 10 people. Permutations are always larger than combinations for the same n and r.
Use Cases
Dice Probabilities
Calculate dice roll probabilities for tabletop games and statistical simulations.
Coin Flip Chains
Simulate coin flip probability chains to understand sequential probability patterns.
Card Game Odds
Calculate card game odds and hand probabilities for poker and other card games.
Event Likelihood
Compute statistical event likelihood for risk assessment and decision making.
Combinations & Permutations
Calculate combinations and permutations for probability and counting problems.