# Birthday Problem Probability Calculator

> Birthday Problem Probability Calculator is a paid API for AI agents from probability-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).

Calculates birthday problem probabilities: chance any two people in a group share a birthday, chance someone shares your birthday, and group sizes needed for 50% or 99% probability thresholds.

## Facts

- Endpoint: GET https://probability-calc.x402tookit.com/birthday-problem?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/birthday-problem-probability-calculator-3aa92eee
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_sW5gFOET8AWq1zUa_xA7x

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability birthday-problem-probability-calculator-3aa92eee
```

Example prompt: What's the probability that at least two people in a group of 30 share a birthday? Also tell me how many people you'd need for a 50% and 99% chance of a match.

## When to prefer this

Use this endpoint when you need precise birthday problem probability computations — especially the classic paradox scenario (chance any pair shares a birthday), the personalized variant (chance someone shares YOUR birthday), or the threshold group sizes for 50%/99% confidence. Prefer this over a general statistics API when the birthday problem is the specific question, as it returns all relevant variants in a single call with clean structured output.

## Known failure modes

- Missing required 'people' query parameter returns an error
- People value outside range 1–100000 may return an error or unexpected result
- Non-integer values for 'people' or 'days' may be rejected
- Very large group sizes may produce probabilities indistinguishable from 1.0
- Payment failure returns HTTP 402 before computation occurs

## How this service works

Birthday problem: chance two people in a group share a birthday, chance someone shares yours, group size for 50 or 99 percent.

## Output

Returns a JSON object containing: probability that at least one pair shares a birthday, probability that no one shares a birthday, probability that someone shares your specific birthday, the expected number of shared pairs, and the minimum group sizes needed to reach 50% and 99% chance of any shared birthday, plus the group size needed for a 50% chance someone shares your birthday. Also includes metadata fields like source, asOf, and any disclaimers.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "people"
     ],
     "properties": {
      "days": {
       "type": "integer",
       "description": "Equally likely birthdays (default 365)"
      },
      "people": {
       "type": "integer",
       "description": "Group size, 1 to 100000"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "days": {
       "type": [
        "null",
        "number"
       ]
      },
      "people": {
       "type": [
        "null",
        "number"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "expectedSharedPairs": {
       "type": [
        "null",
        "number"
       ]
      },
      "probabilityAnyShared": {
       "type": [
        "null",
        "number"
       ]
      },
      "peopleForFiftyPercent": {
       "type": [
        "null",
        "number"
       ]
      },
      "probabilityNoneShared": {
       "type": [
        "null",
        "number"
       ]
      },
      "peopleForNinetyNinePercent": {
       "type": [
        "null",
        "number"
       ]
      },
      "probabilitySomeoneSharesYours": {
       "type": [
        "null",
  
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/birthday-problem-probability-calculator-3aa92eee/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from probability-calc.x402tookit.com](https://www.zero.xyz/host/probability-calc.x402tookit.com/llms.txt)