Probability Calculator
Calculate basic probability, complements, independent events, unions, and conditional probability using decimals, percentages, or fractions.
Probability inputs can be entered as decimals, percentages, or fractions. Examples: 0.25, 25%, or 1/4.
Results
Important Note: Probability results depend on the assumptions behind the event. Independent-event calculations should only be used when one event does not affect the other. For dependent events, real-world probability may require conditional probability, historical data, or a more detailed statistical model.
Use this Probability Calculator to solve basic probability problems and estimate complements, independent events, unions, and conditional probability. Results can be displayed as decimals, percentages, fractions, and odds.
Reviewed by: AjaxCalculators Editorial Team
Last updated: May 2026
Method source: Standard probability formulas and event rules
Editorial standards: Built using transparent formulas, examples, assumptions, and educational explanations.
What Is Probability?
Probability measures the likelihood that an event will occur. Probability values generally range from 0 to 1.
- 0 = impossible event
- 1 = certain event
- 0.5 = equally likely
Probability can also be written as percentages or fractions.
Basic Probability Formula
P(Event) = Favorable outcomes ÷ Total outcomes
Example:
If a die has six sides and you want the probability of rolling a 3:
P(3)=1/6
=0.1667
=16.67%
Common Probability Formulas
Complement Rule
P(Not A)=1−P(A)
Independent Events
P(A and B)=P(A)×P(B)
Union Formula
P(A or B)=P(A)+P(B)−P(A∩B)
Conditional Probability
P(A|B)=P(A∩B)÷P(B)
Probability Interpretation Guide
| Probability | General Meaning |
|---|---|
| 0 | Impossible |
| 0–0.25 | Unlikely |
| 0.5 | Equally likely |
| 0.75–1 | Very likely |
| 1 | Certain |
Worked Example
| Input | Value |
|---|---|
| Favorable outcomes | 3 |
| Total outcomes | 12 |
Formula:
P(event)=3÷12
=0.25
=25%
Complement:
1−0.25=0.75
Common Event Examples
| Event Type | Example |
|---|---|
| Basic probability | Drawing a red card |
| Independent events | Coin toss and dice roll |
| Conditional probability | Probability of rain given clouds |
| Union event | Event A or Event B |
Independent vs Mutually Exclusive Events
| Concept | Meaning |
|---|---|
| Independent | One event does not affect another |
| Mutually exclusive | Events cannot happen simultaneously |
How to Use This Calculator
- Select calculation type.
- Enter probability values or outcomes.
- Enter additional event values if needed.
- Click Calculate.
- Review formulas and results.
Common Mistakes
- Using values outside the 0–1 probability range
- Treating dependent events as independent
- Confusing complements and unions
- Using incorrect event assumptions
Assumptions and Limitations
- Probability depends on assumptions and model structure.
- Results depend on entered values.
- Real-world events can be more complex than simplified models.
Practical Uses
- Statistics education
- Risk estimation
- Gaming probability
- Decision analysis
- Mathematics practice
References
Related Calculators
Frequently Asked Questions
Can probability be greater than 1?
No. Probability values generally stay between 0 and 1.
What does probability 0 mean?
It represents an impossible event.
What does probability 1 mean?
It represents a certain event.
What is the difference between independent and mutually exclusive events?
Independent events do not affect each other. Mutually exclusive events cannot happen together.
Can this calculator solve conditional probability?
Yes. Depending on selected mode, it can estimate multiple probability relationships.
Disclaimer: This Probability Calculator uses standard probability formulas for educational and general estimation purposes. Results depend on accurate input values and correct event assumptions. Calculations may become misleading if dependent events are treated as independent, if events overlap unexpectedly, or if probability values outside the valid 0 to 1 range are used. For real-world risk, finance, health, legal, or safety decisions, use appropriate data and expert guidance.