# Probability Calculator

> Calculate event, complement, combined, and binomial probabilities.

Page: https://freecalculator.tech/tools/probability-calculator
Last reviewed: 2026-10-23

## How do I calculate probability?

A probability is the number of favourable outcomes divided by the number of possible outcomes, between zero and one.

## Formula

P(event)=favorable÷total; P(not A)=1−P(A); independent P(A and B)=P(A)P(B); binomial P(X=k)=C(n,k)p^k(1−p)^(n−k).

- Methodology type: scientific equation.
- Methodology: OpenStax introductory statistics, finite equally likely outcomes, complements, independent events and binomial probability.
- Event counts assume equally likely outcomes. Joint modes require independence. Binomial mode requires independent equal-probability Bernoulli trials and supports up to 170 trials; no distribution is inferred from data.
- P(event)=favorable÷total; P(not A)=1−P(A); independent P(A and B)=P(A)P(B); binomial P(X=k)=C(n,k)p^k(1−p)^(n−k).
- Inputs used: Calculation, Favorable outcomes, Total outcomes, Probability A / success, Probability B, Number of trials, Exact successes.
- Edge handling: Favorable outcomes is required.; Favorable outcomes cannot be negative.; Total outcomes is required.; Total outcomes must be greater than zero.; Probability A / success is required..

## Inputs

- Calculation
- Favorable outcomes
- Total outcomes
- Probability A / success
- Probability B
- Number of trials
- Exact successes

## Worked example: Exactly 5 successes in 10 trials

At p=0.5, the probability is 0.24609375.
1. Start with Calculation: binomial, Favorable outcomes: 1, Total outcomes: 6, Probability A / success: 0.5, Probability B: 0.5, Number of trials: 10.
2. Apply the method: P(event)=favorable÷total; P(not A)=1−P(A); independent P(A and B)=P(A)P(B); binomial P(X=k)=C(n,k)p^k(1−p)^(n−k).
3. At p=0.5, the probability is 0.24609375.

## Common questions

### How do I calculate probability?

A probability is the number of favourable outcomes divided by the number of possible outcomes, between zero and one. Check the formula, example, and limitations on this page before using the result for a real math decision.

### What does independent mean?

One event does not change the probability of the other. Check the formula, example, and limitations on this page before using the result for a real math decision.

### How should probabilities be entered?

Use decimals from 0 to 1, such as 0.25 for 25%. Check the formula, example, and limitations on this page before using the result for a real math decision.

### Does binomial mode infer independence or success probability?

No. You supply success probability and must justify independent identical Bernoulli trials; the tool supports up to 170 trials.

### How do I use the Probability Calculator?

Enter the required values for Calculation, Favorable outcomes, Total outcomes, Probability A / success, Probability B, and the other fields shown. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Probability Calculator use?

P(event)=favorable÷total; P(not A)=1−P(A); independent P(A and B)=P(A)P(B); binomial P(X=k)=C(n,k)p^k(1−p)^(n−k). The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

## Limitations and assumptions

- Only the named probability models; assumptions must be justified externally.
- Binomial computation supports at most 170 trials; no inferred demand or medical risk model.
- For education and operational analysis only. No diagnosis, treatment recommendations, prescribing, dosing instructions, or reimbursement entitlement. Scientific calculations require appropriate laboratory verification; operational estimates do not replace local clinical, safety or financial policies.
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this probability calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- OpenStax — https://openstax.org/books/introductory-statistics-2e/pages/1-introduction

## Cite this page

- APA: Free Calculator. (2026, October 23). Probability Calculator. https://freecalculator.tech/tools/probability-calculator
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