{
  "id": "probability-calculator",
  "version": "2.0.0",
  "name": "Probability Calculator",
  "shortName": "Probability",
  "description": "Calculate independent-event relationships, repeated-event probabilities, normal-distribution areas, or binomial probabilities.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "probability",
    "independent events",
    "union probability",
    "intersection probability",
    "normal distribution",
    "binomial distribution"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "migrated",
  "migratedDate": "2026-08-25",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/probability-calculator.json",
    "qualifiedReview": "pending",
    "qualifiedReviewer": null,
    "qualifiedReviewDate": null,
    "formulaVersion": "2.0.0",
    "referenceCoverage": "references-listed",
    "releaseTestScope": "Catalog and regression checks are not a professional formula audit; consult release evidence.",
    "historicalMetadataDate": "2026-08-25",
    "historicalMetadataNotice": "The imported date is not evidence of a completed human review."
  },
  "urls": {
    "page": "/calculator/probability-calculator/",
    "definition": "/calculator/probability-calculator/definition.json",
    "schema": "/calculator/probability-calculator/schema.json",
    "llms": "/calculator/probability-calculator/llms.txt",
    "legacyDefinition": "/calculator/probability-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/probability-calculator/?mode=two-events&probabilityA=0.5&probabilityB=0.4",
  "queryParameters": {
    "mode": {
      "label": "Probability model",
      "type": "select",
      "required": true,
      "default": "two-events"
    },
    "probabilityA": {
      "label": "Probability of A",
      "type": "number",
      "required": true,
      "default": 0.5,
      "showWhen": {
        "field": "mode",
        "equals": "two-events"
      }
    },
    "probabilityB": {
      "label": "Probability of B",
      "type": "number",
      "required": true,
      "default": 0.4,
      "showWhen": {
        "field": "mode",
        "equals": "two-events"
      }
    },
    "seriesProbabilityA": {
      "label": "Event A probability",
      "type": "number",
      "required": true,
      "default": 0.5,
      "showWhen": {
        "field": "mode",
        "equals": "repeated-events"
      }
    },
    "seriesRepeatsA": {
      "label": "Event A repeat count",
      "type": "number",
      "required": true,
      "default": 3,
      "showWhen": {
        "field": "mode",
        "equals": "repeated-events"
      }
    },
    "seriesProbabilityB": {
      "label": "Event B probability",
      "type": "number",
      "required": true,
      "default": 0.4,
      "showWhen": {
        "field": "mode",
        "equals": "repeated-events"
      }
    },
    "seriesRepeatsB": {
      "label": "Event B repeat count",
      "type": "number",
      "required": true,
      "default": 2,
      "showWhen": {
        "field": "mode",
        "equals": "repeated-events"
      }
    },
    "normalMean": {
      "label": "Mean (μ)",
      "type": "number",
      "required": true,
      "default": 0,
      "showWhen": {
        "field": "mode",
        "equals": "normal"
      }
    },
    "normalStandardDeviation": {
      "label": "Standard deviation (σ)",
      "type": "number",
      "required": true,
      "default": 1,
      "showWhen": {
        "field": "mode",
        "equals": "normal"
      }
    },
    "leftBound": {
      "label": "Left bound",
      "type": "text",
      "required": true,
      "default": "-1",
      "showWhen": {
        "field": "mode",
        "equals": "normal"
      }
    },
    "rightBound": {
      "label": "Right bound",
      "type": "text",
      "required": true,
      "default": "1",
      "showWhen": {
        "field": "mode",
        "equals": "normal"
      }
    },
    "trials": {
      "label": "Number of trials (n)",
      "type": "number",
      "required": true,
      "default": 10,
      "showWhen": {
        "field": "mode",
        "equals": "binomial"
      }
    },
    "successProbability": {
      "label": "Probability of success (p)",
      "type": "number",
      "required": true,
      "default": 0.5,
      "showWhen": {
        "field": "mode",
        "equals": "binomial"
      }
    },
    "successes": {
      "label": "Number of successes (x)",
      "type": "number",
      "required": true,
      "default": 5,
      "showWhen": {
        "field": "mode",
        "equals": "binomial"
      }
    }
  },
  "inputs": [
    {
      "id": "mode",
      "label": "Probability model",
      "type": "select",
      "required": true,
      "defaultValue": "two-events",
      "options": [
        {
          "label": "Two independent events",
          "value": "two-events"
        },
        {
          "label": "Repeated independent events",
          "value": "repeated-events"
        },
        {
          "label": "Normal distribution interval",
          "value": "normal"
        },
        {
          "label": "Binomial distribution",
          "value": "binomial"
        }
      ],
      "width": "full"
    },
    {
      "id": "probabilityA",
      "label": "Probability of A",
      "type": "number",
      "required": true,
      "defaultValue": 0.5,
      "min": 0,
      "max": 1,
      "step": 0.001,
      "showWhen": {
        "field": "mode",
        "equals": "two-events"
      },
      "width": "half"
    },
    {
      "id": "probabilityB",
      "label": "Probability of B",
      "type": "number",
      "required": true,
      "defaultValue": 0.4,
      "min": 0,
      "max": 1,
      "step": 0.001,
      "showWhen": {
        "field": "mode",
        "equals": "two-events"
      },
      "width": "half"
    },
    {
      "id": "seriesProbabilityA",
      "label": "Event A probability",
      "type": "number",
      "required": true,
      "defaultValue": 0.5,
      "min": 0,
      "max": 1,
      "step": 0.001,
      "showWhen": {
        "field": "mode",
        "equals": "repeated-events"
      },
      "width": "half"
    },
    {
      "id": "seriesRepeatsA",
      "label": "Event A repeat count",
      "type": "number",
      "required": true,
      "defaultValue": 3,
      "min": 0,
      "max": 10000,
      "step": 1,
      "showWhen": {
        "field": "mode",
        "equals": "repeated-events"
      },
      "width": "half"
    },
    {
      "id": "seriesProbabilityB",
      "label": "Event B probability",
      "type": "number",
      "required": true,
      "defaultValue": 0.4,
      "min": 0,
      "max": 1,
      "step": 0.001,
      "showWhen": {
        "field": "mode",
        "equals": "repeated-events"
      },
      "width": "half"
    },
    {
      "id": "seriesRepeatsB",
      "label": "Event B repeat count",
      "type": "number",
      "required": true,
      "defaultValue": 2,
      "min": 0,
      "max": 10000,
      "step": 1,
      "showWhen": {
        "field": "mode",
        "equals": "repeated-events"
      },
      "width": "half"
    },
    {
      "id": "normalMean",
      "label": "Mean (μ)",
      "type": "number",
      "required": true,
      "defaultValue": 0,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "normal"
      },
      "width": "half"
    },
    {
      "id": "normalStandardDeviation",
      "label": "Standard deviation (σ)",
      "type": "number",
      "required": true,
      "defaultValue": 1,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "normal"
      },
      "width": "half"
    },
    {
      "id": "leftBound",
      "label": "Left bound",
      "type": "text",
      "required": true,
      "defaultValue": "-1",
      "help": "Use -inf for negative infinity.",
      "showWhen": {
        "field": "mode",
        "equals": "normal"
      },
      "width": "half"
    },
    {
      "id": "rightBound",
      "label": "Right bound",
      "type": "text",
      "required": true,
      "defaultValue": "1",
      "help": "Use inf for positive infinity.",
      "showWhen": {
        "field": "mode",
        "equals": "normal"
      },
      "width": "half"
    },
    {
      "id": "trials",
      "label": "Number of trials (n)",
      "type": "number",
      "required": true,
      "defaultValue": 10,
      "min": 0,
      "max": 1000,
      "step": 1,
      "showWhen": {
        "field": "mode",
        "equals": "binomial"
      },
      "width": "half"
    },
    {
      "id": "successProbability",
      "label": "Probability of success (p)",
      "type": "number",
      "required": true,
      "defaultValue": 0.5,
      "min": 0,
      "max": 1,
      "step": 0.001,
      "showWhen": {
        "field": "mode",
        "equals": "binomial"
      },
      "width": "half"
    },
    {
      "id": "successes",
      "label": "Number of successes (x)",
      "type": "number",
      "required": true,
      "defaultValue": 5,
      "min": 0,
      "max": 1000,
      "step": 1,
      "showWhen": {
        "field": "mode",
        "equals": "binomial"
      },
      "width": "full"
    }
  ],
  "outputs": [
    {
      "id": "primaryProbability",
      "label": "Primary probability",
      "format": "percent",
      "primary": true,
      "digits": 6
    },
    {
      "id": "intersection",
      "label": "P(A ∩ B)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "union",
      "label": "P(A ∪ B)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "exclusiveOr",
      "label": "Exactly one event",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "neither",
      "label": "Neither event",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "complementA",
      "label": "P(A′)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "complementB",
      "label": "P(B′)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "secondaryProbability",
      "label": "Secondary probability",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "exactProbability",
      "label": "P(X = x)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "atMostProbability",
      "label": "P(X ≤ x)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "atLeastProbability",
      "label": "P(X ≥ x)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "expectedValue",
      "label": "Expected value",
      "format": "number",
      "digits": 6
    },
    {
      "id": "variance",
      "label": "Variance",
      "format": "number",
      "digits": 6
    }
  ],
  "formula": {
    "expression": "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."
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "mode": "two-events",
        "probabilityA": 0.5,
        "probabilityB": 0.4,
        "seriesProbabilityA": 0.5,
        "seriesRepeatsA": 3,
        "seriesProbabilityB": 0.4,
        "seriesRepeatsB": 2,
        "normalMean": 0,
        "normalStandardDeviation": 1,
        "leftBound": "-1",
        "rightBound": "1",
        "trials": 10,
        "successProbability": 0.5,
        "successes": 5
      }
    }
  ],
  "sources": [
    {
      "label": "Calculator.net reference calculator",
      "url": "https://www.calculator.net/probability-calculator.html"
    }
  ]
}