# Probability Calculator

> Calculate independent-event relationships, repeated-event probabilities, normal-distribution areas, or binomial probabilities.

Page: https://askcalculators.com/calculator/probability-calculator/
Definition: https://askcalculators.com/calculator/probability-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/probability-calculator/schema.json
Version: 2.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/probability-calculator/?mode=two-events&probabilityA=0.5&probabilityB=0.4

## Inputs
- mode: Probability model; type=select; required; default=two-events; values=two-events|repeated-events|normal|binomial
- probabilityA: Probability of A; type=number; required; default=0.5; min=0; max=1; showWhen=mode:two-events
- probabilityB: Probability of B; type=number; required; default=0.4; min=0; max=1; showWhen=mode:two-events
- seriesProbabilityA: Event A probability; type=number; required; default=0.5; min=0; max=1; showWhen=mode:repeated-events
- seriesRepeatsA: Event A repeat count; type=number; required; default=3; min=0; max=10000; showWhen=mode:repeated-events
- seriesProbabilityB: Event B probability; type=number; required; default=0.4; min=0; max=1; showWhen=mode:repeated-events
- seriesRepeatsB: Event B repeat count; type=number; required; default=2; min=0; max=10000; showWhen=mode:repeated-events
- normalMean: Mean (μ); type=number; required; default=0; showWhen=mode:normal
- normalStandardDeviation: Standard deviation (σ); type=number; required; default=1; min=0.000001; showWhen=mode:normal
- leftBound: Left bound; type=text; required; default=-1; showWhen=mode:normal
- rightBound: Right bound; type=text; required; default=1; showWhen=mode:normal
- trials: Number of trials (n); type=number; required; default=10; min=0; max=1000; showWhen=mode:binomial
- successProbability: Probability of success (p); type=number; required; default=0.5; min=0; max=1; showWhen=mode:binomial
- successes: Number of successes (x); type=number; required; default=5; min=0; max=1000; showWhen=mode:binomial

## Outputs
- primaryProbability: Primary probability; format=percent; primary
- intersection: P(A ∩ B); format=percent
- union: P(A ∪ B); format=percent
- exclusiveOr: Exactly one event; format=percent
- neither: Neither event; format=percent
- complementA: P(A′); format=percent
- complementB: P(B′); format=percent
- secondaryProbability: Secondary probability; format=percent
- exactProbability: P(X = x); format=percent
- atMostProbability: P(X ≤ x); format=percent
- atLeastProbability: P(X ≥ x); format=percent
- expectedValue: Expected value; format=number
- variance: Variance; format=number

## Formula
Independent events: P(A∩B)=P(A)P(B), P(A∪B)=P(A)+P(B)−P(A∩B); normal areas use Φ(z); binomial P(X=x)=C(n,x)pˣ(1−p)ⁿ⁻ˣ.

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.