# Probability calculator

- Human page: https://happytails.ai/en/calculators/probability-calculator/
- Markdown: https://happytails.ai/en/calculators/probability-calculator.md
- Structured JSON: https://happytails.ai/agents/en/calculators/probability-calculator/index.json
- Visibility: public

## Tool capabilities

| Property | Value |
| --- | --- |
| Tool ID | `probability-calculator` |
| Category | calculators |
| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |
| Browser execution | Automatic updates after valid input or file selection. |
| Browser processing | Browser; see tool notes for network behavior. |
| HTTP API | Not callable through HTTP. |
| Browser-agent interface | run_current_tool |

### Implementation notes

Calculate complements, unions, intersections and conditional probabilities. Independence is an explicit assumption. A conditional probability is undefined if its conditioning event has probability zero.

### Inputs and settings

No free-text input is required. Use the file inputs and/or settings below.

| Setting | Meaning | Control type | Default | Constraints |
| --- | --- | --- | --- | --- |
| `a` | Probability of A (%) | number | 30 | min=0 max=100 step=any |
| `b` | Probability of B (%) | number | 40 | min=0 max=100 step=any |
| `method` | Relationship between events | select | "Assume independence" | Allowed: Assume independence, Supply intersection |
| `intersection` | Probability of both A and B (%) | number | 12 | min=0 max=100 step=any |

### Browser-agent workflow

1. Open the human page in a browser that supports WebMCP.
2. Discover the interface exposed by that page; use its actual schema.
3. Select files on the page first when the tool requires files.
4. Call `run_current_tool` with valid input and settings.
5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.

Calls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.

### Planning specification

Enter probabilities from 0 to 100%. The supplied intersection must satisfy the Fréchet bounds. Independence is used only when explicitly selected. Conditional probabilities with a zero denominator are undefined, not zero.

This describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.

### Complete machine-readable capability record

```json
{
  "id": "probability-calculator",
  "category": "calculators",
  "built": true,
  "requirements": "Enter probabilities from 0 to 100%. The supplied intersection must satisfy the Fréchet bounds. Independence is used only when explicitly selected. Conditional probabilities with a zero denominator are undefined, not zero.",
  "implementation": {
    "fields": [
      {
        "key": "a",
        "label": "Probability of A (%)",
        "value": 30,
        "type": "number",
        "min": 0,
        "max": 100,
        "step": "any"
      },
      {
        "key": "b",
        "label": "Probability of B (%)",
        "value": 40,
        "type": "number",
        "min": 0,
        "max": 100,
        "step": "any"
      },
      {
        "key": "method",
        "label": "Relationship between events",
        "value": "Assume independence",
        "type": "select",
        "values": [
          "Assume independence",
          "Supply intersection"
        ]
      },
      {
        "key": "intersection",
        "label": "Probability of both A and B (%)",
        "value": 12,
        "type": "number",
        "min": 0,
        "max": 100,
        "step": "any",
        "showWhen": {
          "method": [
            "Supply intersection"
          ]
        }
      }
    ],
    "note": "Calculate complements, unions, intersections and conditional probabilities. Independence is an explicit assumption. A conditional probability is undefined if its conditioning event has probability zero.",
    "input": false,
    "live": true,
    "presentation": "metrics",
    "background": false,
    "inputMaxLength": 1000000,
    "inputErrorCode": "STAT_SIZE",
    "experience": {
      "automatic": true,
      "single": false,
      "inputMaxLength": 1000000,
      "inputMode": "text",
      "label": "Your text",
      "placeholder": "Type or paste your input…",
      "help": "Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.",
      "action": null
    },
    "mode": "automatic",
    "interactive": false
  },
  "execution": "Browser interface",
  "api": null,
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}
```

## Page guide

Calculate intersections, unions, complements and conditional probabilities for two events.

How can we improve this tool?

Report a problem or share an idea.

Please leave out private information. Your message and the tool name go to our team via PostHog.

### How to use Probability calculator

1. Enter the observations or summary values.
2. Choose the method and check its assumptions.
3. Review the result and download the calculation.

## Useful next steps

- [Multiple testing correction](https://happytails.ai/en/calculators/multiple-testing-correction/) ([Markdown](https://happytails.ai/en/calculators/multiple-testing-correction.md))

- [Pooled summary statistics](https://happytails.ai/en/calculators/pooled-summary-statistics/) ([Markdown](https://happytails.ai/en/calculators/pooled-summary-statistics.md))

## Choose the model before reading the result

Calculate intersections, unions, complements and conditional probabilities for two events.

### Check the assumptions

Enter probabilities from 0 to 100%. The supplied intersection must satisfy the Fréchet bounds. Independence is used only when explicitly selected. Conditional probabilities with a zero denominator are undefined, not zero.

### Keep the calculation

Download the JSON for unrounded results and settings, CSV for the table, and the separate assumptions note. The calculation runs in your browser.