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Probability Calculator

· Last updated：2026-04-30

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

Details

What this tool helps you do

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.

Execution

Run this tool

Fill in the form, run the tool, and review the result in one place.

Samples

Examples that match this tool

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Written by the Elysia Tools team
Math502

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Math & Numbers
Input types
number, select
Output type
json
Sample coverage
4
API ready
Yes

Overview

The Probability Calculator is a straightforward utility designed to compute common probability operations, including unions, independent intersections, complements, and at-least-one scenarios. By accepting inputs as either percentages or proportions, it instantly generates accurate statistical results for risk assessment, data analysis, and academic use.

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

  1. 1Enter the value for Probability A, and if required by your chosen operation, Probability B.
  2. 2Select your input scale, choosing between percentages (e.g., 40) or proportions (e.g., 0.4).
  3. 3Choose the desired mathematical operation, such as Union, Independent Intersection, Complement, or At Least One.
  4. 4Set 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.

Examples

1. Calculating Independent Union Probability

Data Analyst

Background

An analyst is reviewing two independent marketing channels. Channel A has a 40% conversion chance, and Channel B has a 25% chance.

Problem

Find the probability that a user converts through either Channel A or Channel B.

How to use

Enter 40 for Probability A and 25 for Probability B. Set the input scale to 'Percent' and select the 'Union P(A or B)' operation.

Outcome

The tool outputs a combined probability of 0.55, meaning there is a 55% chance of conversion from either channel.

2. Finding the Complement of an Event

Quality Assurance Engineer

Background

A manufacturing process has a known defect rate of 0.03 (proportion).

Problem

Calculate the probability that a manufactured part is completely defect-free.

How to use

Input 0.03 as Probability A, change the input scale to 'Proportion', and select the 'Complement P(not A)' operation.

Outcome

The calculator returns a probability of 0.97 (or 97%), representing the likelihood of a defect-free part.

FAQ

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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