Probability Calculator Calculate simple probability, union, intersection, conditional probability, and complement.

$Probability Calculator illustration$

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Probability Calculator

Calculate simple probability, union, intersection, conditional probability, and complement.

Choose Mode

Select from simple probability, union, intersection, conditional, or complement.

Enter Values

Input the required probability values or favorable/total outcomes.

Get Result

View the calculated probability as a decimal, percentage, and formula.

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What Is Probability Calculator?

A probability calculator helps you compute the likelihood of events occurring. This tool supports five calculation modes: (1) Simple probability — P(A) = favorable outcomes / total outcomes. (2) Union — P(A∪B) = P(A) + P(B) − P(A∩B), the probability that either event occurs. (3) Intersection — P(A∩B), the probability that both events occur simultaneously. (4) Conditional — P(A|B) = P(A∩B) / P(B), the probability of A given that B has occurred. (5) Complement — P(A') = 1 − P(A), the probability that A does NOT occur. Probability theory is the mathematical foundation of statistics, risk analysis, machine learning, genetics, insurance, gambling, and decision-making. Understanding these fundamental operations is essential for anyone working with uncertain events or data-driven decisions.

Why Use Probability Calculator?

Five calculation modes covering all fundamental probability operations
Shows formulas alongside results for learning
Handles both independent and dependent events
Displays results as decimal, percentage, and odds
Clear input labels guide you through each calculation type

Common Use Cases

Statistics Courses

Solve probability homework involving unions, intersections, and conditional probability.

Risk Assessment

Calculate the likelihood of combined events for business risk analysis.

Games & Gambling

Compute odds of specific outcomes in dice, cards, or lottery scenarios.

Quality Control

Determine defect probabilities and combined failure rates.

Technical Guide

Probability is a real number between 0 (impossible) and 1 (certain). The addition rule for union is P(A∪B) = P(A) + P(B) − P(A∩B), where the subtraction prevents double-counting the intersection. For independent events (where A doesn't affect B), P(A∩B) = P(A) × P(B). For dependent events, P(A∩B) = P(A|B) × P(B). Conditional probability, derived from Bayes' theorem, is P(A|B) = P(A∩B) / P(B), provided P(B) > 0. The complement rule states P(A') = 1 − P(A), which is useful when calculating "at least one" probabilities via P(at least one) = 1 − P(none). The calculator accepts probabilities between 0 and 1, validates that combined probabilities don't exceed bounds, and for simple probability mode, computes the ratio of favorable to total outcomes. All results are shown with up to 6 decimal places and as a percentage.

Tips & Best Practices

1
Probabilities must be between 0 and 1 (or 0% to 100%)
2
For "at least one" problems, use 1 − P(none)
3
Independent events: P(A∩B) = P(A) × P(B)
4
For dependent events, you must specify P(A∩B) explicitly
5
The complement is useful: P(A) = 1 − P(not A)

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Frequently Asked Questions

Q What is the difference between independent and dependent events?

Independent events don't affect each other's probability (like two coin flips). Dependent events do (like drawing cards without replacement).

Q What is conditional probability?

P(A|B) is the probability of A occurring given that B has already occurred. It equals P(A∩B)/P(B) and is central to Bayes' theorem.

Q Can two probabilities add up to more than 1?

Individual probabilities can sum to more than 1, but P(A∪B) never exceeds 1. The union formula subtracts the intersection to prevent this.

Q What are odds vs probability?

Probability is favorable/total (e.g., 1/6 for a die). Odds are favorable:unfavorable (e.g., 1:5 for a die). Odds of 3:2 equals probability 3/5 = 0.6.

Q How do I handle "or" vs "and" in probability?

"Or" uses the union formula (addition rule). "And" uses the intersection (multiplication rule). "Or" gives a larger probability; "and" gives a smaller one.

About This Tool

Probability Calculator is a free online tool by FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration or installation required.