---
title: Work an At-Least-k Draw Probability from a Finite Pool Without Replacement — Free
description: Drawing three counters from a small jar changes what remains after each draw. Keep the finite population, marked count, draw count and at-least requirement together before using an independent-draw shortcut in a probability exercise.
category: learning
last_verified: 2026-10-01
freshness: green
published: 2026-10-01
canonical_url: https://gratis-ai.pages.dev/articles/without-replacement-draw-probability.html
companion_app_url: https://gratis-ai.pages.dev/apps/without-replacement-draw-probability.html
reading_time_minutes: 10
tags: learning, hyperdraw, local-first, explicit-assumptions, no-account
---

# Work an At-Least-k Draw Probability from a Finite Pool Without Replacement — Free

Drawing three counters from a small jar changes what remains after each draw. Keep the finite population, marked count, draw count and at-least requirement together before using an independent-draw shortcut in a probability exercise.

**Free and complete.** This guide is a standalone free tool — no account, no card, anywhere. The only paid option is one optional extra outcome: $4 one-time. Nothing in the free tier is gated.

## Who it's for

Learners checking finite-pool probability exercises

## What's free

- one complete unwatermarked draw-probability dial run in the app
- three labeled samples and unlimited article-demo calculations
- complete result text and a user-triggered input-state link

## Optional paid add-on

**$4 one-time.**

- unlimited subsequent draw-probability dial app calculations after a local convenience signal
- print the draw-probability dial with visible assumptions and its safety boundary
- CSV of the displayed % probability and row workings; conditional estimate uses your manual-retyping minutes
- five local reading summaries (headline/count/time), not saved full inputs or cross-device backups

## Sources & verification

- Tool: GratisAI local-first instrument (no key, no account)
- Primary source: the free tool itself (local-first, no external dependency)
- Last verification: 2026-10-01 (green)

## Use it

- Interactive guide: https://gratis-ai.pages.dev/articles/without-replacement-draw-probability.html
- Companion app: https://gratis-ai.pages.dev/apps/without-replacement-draw-probability.html
- This machine-readable mirror: /mirrors/without-replacement-draw-probability.md

*Generated free at https://gratis-ai.pages.dev/articles/without-replacement-draw-probability.html — every guide on GratisAI is a complete, working tool. $0, no account, no card, anywhere.*