Math & Statistics
Probability & Combinatorics Calculator
Updated Sep 3, 2026 Reviewed Sep 3, 2026
Calculate event odds and complements, two-event unions and intersections, exact or cumulative binomial probabilities, and BigInt-safe permutations and combinations.
Chance and counting
Choose a probability model
Result
Calculation summary
Enter values to see the result
Your result, breakdown, assumptions, and warnings will appear here.
Probability model
Events and outcomes
Formula
P(E)=f/t
How to use this calculator
- 1Choose an event, binomial, or counting mode.
- 2Enter required counts or probabilities.
- 3Review complementary, cumulative, or exact integer results.
Formula
P(A∪B)=P(A)+P(B)−P(A∩B); C(n,r)=n!/[r!(n−r)!]
Each mode applies the matching probability identity or integer product.
Calculation steps
- Validate counts and probability bounds.
- Apply the selected event or counting formula.
- Return related complementary results and assumptions.
Worked example
Three favorable outcomes among ten equally likely outcomes give 30% probability and odds 3:7.
Assumptions
- Simple outcomes are equally likely.
- Binomial trials are independent with fixed p.
- Two-event mode uses the entered intersection.
Sources
Frequently asked questions
What is a complement?
It is one minus the event probability.
Are two events assumed independent?
No, enter their intersection directly.
What does at least k mean?
It sums outcomes from k through n.
Permutation or combination?
Permutations count order; combinations do not.
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