Distribution Table

{
  "asOf": "2026-10-11T14:44:17.625Z",
  "degraded": false,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "distribution": "hypergeometric",
  "mean": 1.25,
  "mode": 1,
  "notChecked": [
    "sampling with versus without replacement (geometric, binomial and negative binomial assume independent trials; hypergeometric is without replacement)",
    "tables are cut to the first 60 rows or the point where the remaining tail is below 1e-9 (the full cumulative is exact)",
    "…1 more"
  ],
  "parameters": {
    "K": 13,
    "N": 52,
    "n": 5
  },
  "reasons": [
    "Probabilities are computed in log space from exact formulas; columns are pmf, cumulative P(X<=k) and upper tail P(X>=k).",
    "All values assume the stated parameters are exact."
  ],
  "source": "computed locally (exact formulas in log space)",
  "standardDeviation": 0.92950018,
  "summary": "hypergeometric: mean 1.25, variance 0.86397059, sd 0.92950018, mode 1.",
  "support": "k = 0 to 5 (successes in 5 draws without replacement)",
  "table": [
    {
      "cumulative": 0.22153361,
      "k": 0,
      "probability": 0.22153361,
      "upperTail": 1
    },
    {
      "cumulative": 0.63295318,
      "k": 1,
      "probability": 0.41141957,
      "upperTail": 0.77846639
    }
  ],
  "tableComplete": true,
  "variance": 0.86397059,
  "verdict": "TABLE"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://probability-calc.x402tookit.com/distribution-table?K=13&N=52&dist=hypergeometric&n=5'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://probability-calc.x402tookit.com/distribution-table?K=13&N=52&dist=hypergeometric&n=5' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fprobability-calc.x402tookit.com%2Fdistribution-table
const res = await pay("https://probability-calc.x402tookit.com/distribution-table?K=13&N=52&dist=hypergeometric&n=5");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://probability-calc.x402tookit.com/distribution-table?K=13&N=52&dist=hypergeometric&n=5")
    print(res.status_code, res.text)