Probability Calculator

Calculate the probability of single or multiple events accurately.

Probability Engine

Analyze interactions between independent events A and B.

Probability of AP(A)

Probability of BP(B)

Theorem Checklist

Independence Law

Assumes A and B are independent: P(A ∩ B) = P(A) × P(B).

Addition Rule

Calculates the union as P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Complement Rule

The probability of 'Not A' is always 1 - P(A).

Sample Space

Total probability space must equal 100% (1.00).

Sample Space Map

Visual Outcome Probability

Comparative Odds

Note on Dependency

This model assumes independent events. If event A affects B, conditional probability P(B|A) must be used. Our engine uses standard multiplication P(A)×P(B) as the base case.

Understanding the Probability Calculator

Calculate the mathematical likelihood of events occurring. Our engine analyzes independent events A and B to provide joint probabilities, unions, and sample space mapping.

Guide

How to use the Probability Calculator

1Enter the individual probability of Event A (P(A)) as a decimal between 0 and 1.
2Enter the individual probability of Event B (P(B)).
3Review the breakdown of joint events: P(A ∩ B), P(A ∪ B), and P(A').
4Analyze the Sample Space Map (Treemap) and Comparative Odds bar chart for visual insight.

Applications

Common Use Cases

Risk Assessment: Estimating the likelihood of multiple independent equipment failures.

Finance: Modeling the probability of two independent market events occurring simultaneously.

Gaming: Calculating odds in card games or dice rolls assuming fresh trials.

Weather: Analyzing the chance of localized rain vs. regional precipitation patterns.

The Maths Behind the Calculation

P(A ∩ B) = P(A) × P(B)

For independent events, the intersection (both occurring) is the product of their individual probabilities. The union (either occurring) is P(A) + P(B) - P(A ∩ B).

Knowledge Base

Frequently Asked Questions

What are independent events?

Events are independent if the occurrence of one does not change the probability of the other occurring (e.g., rolling two separate dice).

Why do probabilities only go from 0 to 1?

In mathematics, 0 represents impossibility and 1 represents absolute certainty. Any value in between represents the scale of likelihood.

What is P(A ∪ B)?

This is the union of probabilities, representing the chance that Event A occurs, OR Event B occurs, OR both occur.

Regional Notice: United States

"Federal tax estimates are based on 2024 brackets. Consult a tax professional for official filing."

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