Probability Calculator
The probability of a single event from favorable and possible outcomes, its odds and complement, and the chance of two independent events both happening or either happening.
Probability = favorable outcomes ÷ total outcomes, a number from 0 to 1.
How the probability calculator works
Probability = favorable outcomes ÷ total outcomes, a number from 0 to 1. Odds compare favorable to unfavourable. For two independent events A and B: P(A and B) = P(A) × P(B); P(A or B) = P(A) + P(B) − P(A and B). The complement, 1 − P, is the chance the event does not happen.
Formula: P = favourable / total; P(A and B) = P(A)·P(B); P(A or B) = P(A) + P(B) − P(A)P(B)
Worked examples
| Inputs | P(A) | Note |
|---|---|---|
| rolling a 6 | 16.6667% | 16.67%, odds 1 : 5 |
| a 6 and a head | 16.6667% | and: 8.33%, or: 58.33% |
| drawing a heart | 25% | 25% |
FAQFrequently asked questions
What is the difference between probability and odds?
Probability is favorable ÷ total (1/6 for a six); odds are favorable : unfavourable (1 : 5).
What does independent mean?
One event does not change the chance of the other — a coin and a die, not two cards drawn without replacement.
Why subtract P(A and B) for "or"?
Adding P(A) and P(B) counts the overlap twice; subtracting it corrects that.
Can a probability be more than 1?
No. 0 means impossible and 1 (100%) certain.
What is the chance of at least one success in n tries?
1 − (1 − p)ⁿ. Five rolls for at least one six: 1 − (5/6)⁵ ≈ 60%.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.