Math & StatisticsFormula-based · Runs in your browser

Probability Calculator

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

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Inputs

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Result

Updates as valid inputs change.

Calculated locally
Primary probability
P(A ∩ B)
P(A ∪ B)
Exactly one event
Neither event
P(A′)
P(B′)
Secondary probability
P(X = x)
P(X ≤ x)
P(X ≥ x)
Expected value
Variance

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Calculation steps

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  1. 1

    Formula selected

    The calculator uses the following formula or method.

    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.

  2. 2

    Values entered

    Your values are placed into the calculation.

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  3. 3

    Result calculated

    The formula or method produces the following result values.

    Results will appear after a successful calculation.

  4. 4

    Answer formatted

    Displayed values are rounded and formatted using each output’s configured precision.

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How it works

Calculate independent-event relationships, repeated-event probabilities, normal-distribution areas, or binomial probabilities. Inputs are calculated locally in the browser, and valid values are retained in the page URL for bookmarking.

Input query strings and outputs

Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.

Input query strings

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  • ?mode= Probability model

    Choice · Required · Default: two-events · Accepted values: two-events, repeated-events, normal, binomial

  • ?probabilityA= Probability of A

    Number · Required · Default: 0.5 · Used when mode = two-events

  • ?probabilityB= Probability of B

    Number · Required · Default: 0.4 · Used when mode = two-events

  • ?seriesProbabilityA= Event A probability

    Number · Required · Default: 0.5 · Used when mode = repeated-events

  • ?seriesRepeatsA= Event A repeat count

    Number · Required · Default: 3 · Used when mode = repeated-events

  • ?seriesProbabilityB= Event B probability

    Number · Required · Default: 0.4 · Used when mode = repeated-events

  • ?seriesRepeatsB= Event B repeat count

    Number · Required · Default: 2 · Used when mode = repeated-events

  • ?normalMean= Mean (μ)

    Number · Required · Default: 0 · Used when mode = normal

  • ?normalStandardDeviation= Standard deviation (σ)

    Number · Required · Default: 1 · Used when mode = normal

  • ?leftBound= Left bound

    Text · Required · Default: -1 · Used when mode = normal

  • ?rightBound= Right bound

    Text · Required · Default: 1 · Used when mode = normal

  • ?trials= Number of trials (n)

    Number · Required · Default: 10 · Used when mode = binomial

  • ?successProbability= Probability of success (p)

    Number · Required · Default: 0.5 · Used when mode = binomial

  • ?successes= Number of successes (x)

    Number · Required · Default: 5 · Used when mode = binomial

Outputs

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  • primaryProbability Primary probability

    Percentage · Primary output

  • intersection P(A ∩ B)

    Percentage

  • union P(A ∪ B)

    Percentage

  • exclusiveOr Exactly one event

    Percentage

  • neither Neither event

    Percentage

  • complementA P(A′)

    Percentage

  • complementB P(B′)

    Percentage

  • secondaryProbability Secondary probability

    Percentage

  • exactProbability P(X = x)

    Percentage

  • atMostProbability P(X ≤ x)

    Percentage

  • atLeastProbability P(X ≥ x)

    Percentage

  • expectedValue Expected value

    Number

  • variance Variance

    Number

Formula notes

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.

Input guidance

Use consistent units for every length or measurement in the same calculation. Results are educational mathematical estimates and should be checked before high-stakes use.

Sources
Limitations
  • Results depend on the selected method and input assumptions. Displayed decimals may be rounded; retain appropriate precision for later calculations.