Probability Calculator

Calculate probabilities of independent, dependent, mutually exclusive, and conditional events P(A or B), P(A and B).

Calculator Inputs

Likelihood of A occurring (0 to 1).
Likelihood of B occurring (0 to 1).
Relationship.

Calculated Results

Probability P(A and B)
0.1200 (12.0%)
P(A or B) - Union 0.6800 (68.0%)
P(Neither A nor B) 0.3200 (32.0%)
Odds for Event A 2 to 3 (0.67)
Values calculate live as you adjust inputs.

About Probability Calculator

What is the Probability Calculator?

The Probability Calculator is an enterprise-grade calculation tool designed to compute exact mathematical, financial, or scientific parameters based on peer-reviewed formulas.

How to Use This Calculator

  1. Enter your primary input variables in the input fields above.
  2. Select your desired measurement units or options.
  3. Click Calculate to instantly view live outputs, step-by-step mathematical breakdowns, and formulas.

Mathematical Formula & Derivation

Our calculation engine implements verified equations approved by academic literature, WHO guidelines, IRS tax codes, or BIPM metric standards.

Frequently Asked Questions

Q: Is this calculator free to use?
A: Yes! OmniCalc Ultra provides 100% free, private, client-side calculations with zero tracking.

Scientific & Academic References

  • International System of Units (SI) Standards
  • NIST Engineering & Mathematical Reference Handbooks

What is Probability Calculator?

Computes union, intersection, and complementary probabilities for random events based on Kolmogorov probability axioms.

How to Use This Calculator

  1. Enter decimal probability of event A and B (0 to 1).
  2. Select whether events are independent or mutually exclusive.
  3. Review joint and disjunctive probabilities.

The Mathematical Formula & Variables

P(A and B) = P(A) * P(B); P(A or B) = P(A) + P(B) - P(A and B)

Step-by-Step Worked Example

Scenario: Independent events with P(A) = 0.40 and P(B) = 0.30.

  1. Intersection P(A and B) = 0.40 * 0.30 = 0.12 (12%).
  2. Union P(A or B) = 0.40 + 0.30 - 0.12 = 0.58 (58%).

Result: 12.0% (P of both occurring)

Frequently Asked Questions

What are mutually exclusive events?

Events that cannot happen simultaneously (e.g. flipping heads and tails on a single coin toss). P(A and B) is always 0.