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 modelChoice · Required · Default: two-events · Accepted values: two-events, repeated-events, normal, binomial
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?probabilityA=Probability of ANumber · Required · Default: 0.5 · Used when mode = two-events
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?probabilityB=Probability of BNumber · Required · Default: 0.4 · Used when mode = two-events
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?seriesProbabilityA=Event A probabilityNumber · Required · Default: 0.5 · Used when mode = repeated-events
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?seriesRepeatsA=Event A repeat countNumber · Required · Default: 3 · Used when mode = repeated-events
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?seriesProbabilityB=Event B probabilityNumber · Required · Default: 0.4 · Used when mode = repeated-events
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?seriesRepeatsB=Event B repeat countNumber · Required · Default: 2 · Used when mode = repeated-events
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?normalMean=Mean (μ)Number · Required · Default: 0 · Used when mode = normal
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?normalStandardDeviation=Standard deviation (σ)Number · Required · Default: 1 · Used when mode = normal
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?leftBound=Left boundText · Required · Default: -1 · Used when mode = normal
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?rightBound=Right boundText · Required · Default: 1 · Used when mode = normal
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?trials=Number of trials (n)Number · Required · Default: 10 · Used when mode = binomial
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?successProbability=Probability of success (p)Number · Required · Default: 0.5 · Used when mode = binomial
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?successes=Number of successes (x)Number · Required · Default: 5 · Used when mode = binomial
Outputs
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primaryProbabilityPrimary probabilityPercentage · Primary output
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intersectionP(A ∩ B)Percentage
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unionP(A ∪ B)Percentage
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exclusiveOrExactly one eventPercentage
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neitherNeither eventPercentage
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complementAP(A′)Percentage
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complementBP(B′)Percentage
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secondaryProbabilitySecondary probabilityPercentage
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exactProbabilityP(X = x)Percentage
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atMostProbabilityP(X ≤ x)Percentage
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atLeastProbabilityP(X ≥ x)Percentage
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expectedValueExpected valueNumber
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varianceVarianceNumber
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.