{
  "title": "Bayes theorem visualizer",
  "human_url": "https://happytails.ai/en/calculators/bayes-theorem-visualizer/",
  "agent_url": "https://happytails.ai/agents/en/calculators/bayes-theorem-visualizer/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/bayes-theorem-visualizer.md",
  "content": "Bayes theorem visualizer\nUpdate a prior from stated likelihoods and see every branch of the expected-frequency tree.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nHow to use Bayes theorem visualizer\nEnter the prior probability and the likelihood of the evidence under each hypothesis.\nChoose a reference total to see expected frequencies.\nRead the evidence denominator before using the posterior, and download the full tree.\nUseful next steps\nProbability calculator\nEmpirical distribution viewer\nRead the model\nUpdate a prior from stated likelihoods and see every branch of the expected-frequency tree.\nCheck the definition\nTwo mutually exclusive, exhaustive hypotheses. Enter probabilities from 0 to 100% and a reference total from 1 to one billion. Counts are expectations, not observations or rounded people. A posterior is undefined when its conditioning event has probability zero. This is a calculation from supplied assumptions, not a diagnosis or inferred likelihood.\nKeep the calculation\nDownload SVG for the chart, JSON for unrounded values, CSV for the table and the assumptions note. Your input stays on your device.",
  "content_format": "text/plain",
  "visibility": "public",
  "links": [
    {
      "name": "Probability calculator",
      "url": "https://happytails.ai/en/calculators/probability-calculator/"
    },
    {
      "name": "Empirical distribution viewer",
      "url": "https://happytails.ai/en/calculators/empirical-distribution-viewer/"
    }
  ],
  "tool": {
    "id": "bayes-theorem-visualizer",
    "category": "calculators",
    "built": true,
    "requirements": "Two mutually exclusive, exhaustive hypotheses. Enter probabilities from 0 to 100% and a reference total from 1 to one billion. Counts are expectations, not observations or rounded people. A posterior is undefined when its conditioning event has probability zero. This is a calculation from supplied assumptions, not a diagnosis or inferred likelihood.",
    "implementation": {
      "fields": [
        {
          "key": "prior",
          "label": "Prior probability of A (%)",
          "value": 10,
          "type": "number",
          "min": 0,
          "max": 100,
          "step": "any"
        },
        {
          "key": "likelihood",
          "label": "Probability of evidence given A (%)",
          "value": 80,
          "type": "number",
          "min": 0,
          "max": 100,
          "step": "any"
        },
        {
          "key": "alternative",
          "label": "Probability of evidence given not A (%)",
          "value": 20,
          "type": "number",
          "min": 0,
          "max": 100,
          "step": "any"
        },
        {
          "key": "total",
          "label": "Reference total for expected counts",
          "value": 1000,
          "type": "number",
          "min": 1,
          "max": 1000000000,
          "step": 1
        }
      ],
      "input": false,
      "live": true,
      "presentation": "metrics",
      "note": "State a prior and two likelihoods. The tree shows expected frequencies for your reference total; these are not real observations. A zero-probability conditioning event has no defined posterior.",
      "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"
    }
  },
  "markdown": "# Bayes theorem visualizer\n\n- Human page: https://happytails.ai/en/calculators/bayes-theorem-visualizer/\n- Markdown: https://happytails.ai/en/calculators/bayes-theorem-visualizer.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/bayes-theorem-visualizer/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `bayes-theorem-visualizer` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Automatic updates after valid input or file selection. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | run_current_tool |\n\n### Implementation notes\n\nState a prior and two likelihoods. The tree shows expected frequencies for your reference total; these are not real observations. A zero-probability conditioning event has no defined posterior.\n\n### Inputs and settings\n\nNo free-text input is required. Use the file inputs and/or settings below.\n\n| Setting | Meaning | Control type | Default | Constraints |\n| --- | --- | --- | --- | --- |\n| `prior` | Prior probability of A (%) | number | 10 | min=0 max=100 step=any |\n| `likelihood` | Probability of evidence given A (%) | number | 80 | min=0 max=100 step=any |\n| `alternative` | Probability of evidence given not A (%) | number | 20 | min=0 max=100 step=any |\n| `total` | Reference total for expected counts | number | 1000 | min=1 max=1000000000 step=1 |\n\n### Browser-agent workflow\n\n1. Open the human page in a browser that supports WebMCP.\n2. Discover the interface exposed by that page; use its actual schema.\n3. Select files on the page first when the tool requires files.\n4. Call `run_current_tool` with valid input and settings.\n5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.\n\nCalls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.\n\n### Planning specification\n\nTwo mutually exclusive, exhaustive hypotheses. Enter probabilities from 0 to 100% and a reference total from 1 to one billion. Counts are expectations, not observations or rounded people. A posterior is undefined when its conditioning event has probability zero. This is a calculation from supplied assumptions, not a diagnosis or inferred likelihood.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n  \"id\": \"bayes-theorem-visualizer\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"requirements\": \"Two mutually exclusive, exhaustive hypotheses. Enter probabilities from 0 to 100% and a reference total from 1 to one billion. Counts are expectations, not observations or rounded people. A posterior is undefined when its conditioning event has probability zero. This is a calculation from supplied assumptions, not a diagnosis or inferred likelihood.\",\n  \"implementation\": {\n    \"fields\": [\n      {\n        \"key\": \"prior\",\n        \"label\": \"Prior probability of A (%)\",\n        \"value\": 10,\n        \"type\": \"number\",\n        \"min\": 0,\n        \"max\": 100,\n        \"step\": \"any\"\n      },\n      {\n        \"key\": \"likelihood\",\n        \"label\": \"Probability of evidence given A (%)\",\n        \"value\": 80,\n        \"type\": \"number\",\n        \"min\": 0,\n        \"max\": 100,\n        \"step\": \"any\"\n      },\n      {\n        \"key\": \"alternative\",\n        \"label\": \"Probability of evidence given not A (%)\",\n        \"value\": 20,\n        \"type\": \"number\",\n        \"min\": 0,\n        \"max\": 100,\n        \"step\": \"any\"\n      },\n      {\n        \"key\": \"total\",\n        \"label\": \"Reference total for expected counts\",\n        \"value\": 1000,\n        \"type\": \"number\",\n        \"min\": 1,\n        \"max\": 1000000000,\n        \"step\": 1\n      }\n    ],\n    \"input\": false,\n    \"live\": true,\n    \"presentation\": \"metrics\",\n    \"note\": \"State a prior and two likelihoods. The tree shows expected frequencies for your reference total; these are not real observations. A zero-probability conditioning event has no defined posterior.\",\n    \"experience\": {\n      \"automatic\": true,\n      \"single\": false,\n      \"inputMaxLength\": 1000000,\n      \"inputMode\": \"text\",\n      \"label\": \"Your text\",\n      \"placeholder\": \"Type or paste your input…\",\n      \"help\": \"Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.\",\n      \"action\": null\n    },\n    \"mode\": \"automatic\",\n    \"interactive\": false\n  },\n  \"execution\": \"Browser interface\",\n  \"api\": null,\n  \"browser_agent\": {\n    \"supported\": true,\n    \"name\": \"run_current_tool\",\n    \"discovery\": \"WebMCP on the human page in a supporting browser\",\n    \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n  }\n}\n```\n\n## Page guide\n\nUpdate a prior from stated likelihoods and see every branch of the expected-frequency tree.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n### How to use Bayes theorem visualizer\n\n1. Enter the prior probability and the likelihood of the evidence under each hypothesis.\n2. Choose a reference total to see expected frequencies.\n3. Read the evidence denominator before using the posterior, and download the full tree.\n\n## Useful next steps\n\n- [Probability calculator](https://happytails.ai/en/calculators/probability-calculator/) ([Markdown](https://happytails.ai/en/calculators/probability-calculator.md))\n\n- [Empirical distribution viewer](https://happytails.ai/en/calculators/empirical-distribution-viewer/) ([Markdown](https://happytails.ai/en/calculators/empirical-distribution-viewer.md))\n\n## Read the model\n\nUpdate a prior from stated likelihoods and see every branch of the expected-frequency tree.\n\n### Check the definition\n\nTwo mutually exclusive, exhaustive hypotheses. Enter probabilities from 0 to 100% and a reference total from 1 to one billion. Counts are expectations, not observations or rounded people. A posterior is undefined when its conditioning event has probability zero. This is a calculation from supplied assumptions, not a diagnosis or inferred likelihood.\n\n### Keep the calculation\n\nDownload SVG for the chart, JSON for unrounded values, CSV for the table and the assumptions note. Your input stays on your device.\n"
}