ForHosting KIT · Developer Utilities

Hypergeometric probability

Sampling without replacement is the everyday setting for cards, quality-control lots, and urn models: each draw changes the composition of what remains, so successive trials are not independent.

● BetaFree · in your browser

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Use it from WebAPIEmailTelegramApp soon

When a finite population of size N contains exactly K success states and you draw n items at once or in sequence without putting them back, the chance of observing exactly k successes follows the hypergeometric probability mass function. That formula multiplies the ways to choose k successes from the K good items by the ways to choose the remaining draws from the non-successes, then divides by the ways to choose any sample of size n from the whole population. This capability accepts N, K, n, and k, validates that the parameters are consistent with a legal without-replacement experiment, and returns the probability together with exact binomial coefficients as decimal strings, a short formula string, and the feasible range of k for those N, K, and n. Impossible combinations such as more successes in the sample than exist in the population are rejected with a clear validation error instead of a silent zero. The free browser tool and the paid API share one pure function, so homework demos and automated fixtures never diverge on the same inputs.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/prob/hypergeometric

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/prob/hypergeometric \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"N":52,"K":4,"n":5,"k":2}'

const res = await fetch("https://api.kit.forhosting.com/prob/hypergeometric", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "N": 52,
    "K": 4,
    "n": 5,
    "k": 2
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/prob/hypergeometric",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "N": 52,
    "K": 4,
    "n": 5,
    "k": 2
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/prob/hypergeometric", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"N":52,"K":4,"n":5,"k":2}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"N":52,"K":4,"n":5,"k":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/prob/hypergeometric", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "N": 52,
  "K": 4,
  "n": 5,
  "k": 2
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "prob.hypergeometric",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Limits

`min_N`	0
`max_N`	10000
`min_K`	0
`min_n`	0
`min_k`	0

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Read the full KIT documentation →

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