Probability Calculator

Name: Probability Calculator
Author: Jitendra Kumar

Calculate event probability, complements, two-event overlap, conditional probability, repeated independent trials, and binomial probability.

Last Updated: May 2026

Probability calculation

Favorable outcomes

Example: rolling a 1, 2, or 3 gives 3 favorable outcomes.

Total possible outcomes

All equally likely outcomes in the sample space.

P(A)

30%

Complement

70%

Odds For

3:7

Odds Against

7:3

Step	Formula or result
Formula	P(A) = favorable outcomes / total outcomes
Substitution	3 / 10
Complement	P(not A) = 1 - P(A) = 70%

Decimal or percent

Enter 0.25 or 25 for a 25% probability. Values above 1 and up to 100 are read as percentages.

Overlap matters

For two events, the union subtracts P(A and B) so overlapping outcomes are not double-counted.

Independence

Repeated-trial and binomial modes assume each trial has the same probability and is independent.

Probability setup note

Probability models depend on the sample space and assumptions. Check whether outcomes are equally likely, events overlap, and trials are independent before using the result.

Probability Modeling Notice

This calculator is for educational and planning use. Probability results depend on correct assumptions about the sample space, independence, event overlap, and equal likelihood. Verify assumptions before using outputs for high-stakes decisions.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and founder-led review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Jitendra Kumar, Founder & Editorial Standards Lead, oversees methodology standards and trust-sensitive publishing decisions.

Review editor profile

Topic Ownership

Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology

See ownership standards

Methodology & Updates

Page updated May 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.

Sources & methodology About the review process

How to Use the Probability Calculator

Choose the calculation mode that matches your problem. Use single-event mode when you know favorable and total outcomes, two-event mode when events can overlap, and conditional mode when one event is known to have occurred.

Use repeated-trial or binomial mode only when each trial is independent and has the same probability. Enter probabilities as decimals such as 0.25 or percentages such as 25.

Step 1: Pick a probability mode
Choose single event, two events, conditional probability, repeated trials, or binomial probability.
Step 2: Enter counts or probabilities
Use counts for simple sample spaces or decimals/percentages for probability inputs.
Step 3: Review the primary result
Check the highlighted probability, complement, and related outputs.
Step 4: Audit the formula table
Use the formula rows to confirm overlap, independence, and conditional assumptions.

How This Probability Calculator Works

The calculator applies standard probability rules based on your selected mode. Simple event mode divides favorable outcomes by total outcomes and shows the complement and odds.

Two-event mode uses the addition rule, subtracting the intersection so overlapping outcomes are not counted twice. Conditional mode divides the joint probability by the condition probability.

Repeated-trial and binomial modes assume independent trials. The binomial workflow uses combinations with the success probability and failure probability to calculate exactly, at most, and at least k successes.

Probability Formula Guide

Core Probability Formulas

Concept	Formula	Use
Single event	P(A) = favorable outcomes / total outcomes	Basic equally likely outcome setup.
Complement	P(not A) = 1 - P(A)	Useful for at least-one and no-success problems.
Union	P(A or B) = P(A) + P(B) - P(A and B)	Prevents double-counting overlap.
Conditional	P(A \| B) = P(A and B) / P(B)	Probability of A after B is known to occur.
Repeated trials	P(at least one) = 1 - (1 - p)^n	Assumes independent trials.
Binomial	P(X = k) = C(n,k) p^k (1-p)^(n-k)	Exactly k successes across n independent trials.

Which Mode to Use

Mode	Inputs	Best for
Single event	Favorable and total outcomes	Cards, dice, raffle tickets, simple sample spaces.
Two events	P(A), P(B), and P(A and B)	Either/or probability with overlap.
Conditional	P(A and B) and P(B)	Probability after a condition or filter is applied.
Repeated trials	p and n	Chance of at least one success, none, all, or exactly one.
Binomial	p, n, and target successes k	Exactly, at most, or at least k successes.

The most common probability mistake is using the right formula with the wrong assumption. Before calculating, decide whether the events overlap, whether trials are independent, and whether every outcome in the sample space is equally likely.

For dataset summaries after an experiment, use the statistics calculator. For exact ratios and sample-space fractions, use the fraction calculator.

Keep the research moving with Statistics Calculator, Percentage Calculator, Fraction Calculator, and Scientific Calculator.

Frequently Asked Questions

It solves single-event probability, complements, two-event union and intersection, conditional probability, repeated independent trials, and binomial probability.

Yes. Enter 0.25 or 25 for a 25% probability. Values above 1 and up to 100 are interpreted as percentages.

P(A or B) is the probability that event A happens, event B happens, or both happen. The formula subtracts P(A and B) so overlapping outcomes are not counted twice.

Conditional probability measures the probability of A given that B already happened. It is calculated as P(A and B) divided by P(B).

Use binomial probability when there are a fixed number of independent trials, each trial has the same success probability, and you want the chance of a specific number of successes.