# Probability Calculator

Calculate union, independent intersection, complement, and at-least-one probabilities

> Canonical page: https://elysiatools.com/en/tools/probability-calculator

- **Category:** Math & Numbers

- **Keywords:** probability, union, intersection, complement, at least one, statistics

## Overview

Calculate common probability operations.

Use this tool for complements, independent intersections, independent unions, and at-least-one event probabilities. Inputs can be percentages or proportions.

## Inputs

- **Probability A** (number)
- **Probability B** (number)
- **Input Scale** (select)
- **Operation** (select)
- **Decimal Places** (number)

## When to use

- When determining the likelihood of either event A or event B occurring (Union).
- When calculating the chance of two independent events happening simultaneously (Intersection).
- When finding the exact probability that a specific event will not happen (Complement).

## How it works

- Enter the value for Probability A, and if required by your chosen operation, Probability B.
- Select your input scale, choosing between percentages (e.g., 40) or proportions (e.g., 0.4).
- Choose the desired mathematical operation, such as Union, Independent Intersection, Complement, or At Least One.
- Set your preferred decimal places to view the calculated probability and percentage in the JSON output.

## Use cases

- Evaluating risk by calculating the probability of at least one failure occurring in a system with multiple independent components.
- Determining the combined likelihood of two independent marketing campaigns successfully converting a customer.
- Finding the exact probability of an event not happening for statistical reporting and academic assignments.

## Frequently asked questions

### What is the difference between percent and proportion input scales?

Percentages range from 0 to 100 (e.g., 40%), while proportions are expressed as decimals between 0 and 1 (e.g., 0.40). The calculator supports both formats.

### Does this calculator support dependent events?

No, the intersection and union calculations in this tool assume that Event A and Event B are completely independent of each other.

### What does the Complement operation do?

The complement calculates the probability that Event A will not occur, which is mathematically expressed as 1 minus the probability of Event A.

### How does the At Least One operation work?

It calculates the probability that at least one of the independent events occurs. This is particularly useful for risk assessment and reliability testing.

### Can I adjust the precision of the results?

Yes, you can use the decimal places setting to round your final probability and percentage outputs to your desired level of precision, up to 10 decimal places.

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