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draw-probability dial · meter band gauge

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

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.

1 · Pool code | total objects | marked objects | objects drawn

FIRST-LOAD

HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.

Data note: The draw-probability dial processes Pool code | total objects | marked objects | objects drawn locally. Starter/sample selection and Run compute in this tab; no input is sent by the calculator. A local draft may be saved; explicit state-link sharing or optional external AI formatting can disclose inputs. Use non-sensitive labels.

Perspective: Before: repeated draws were treated as independent by habit. After: finite composition and the full at-least event have explicit combinatorial workings.

2 · Read the draw-probability dial

Finite-pool probability exercise only, not a prediction, gambling strategy or proof that an observed selection was fair. Confirm the sampling mechanism and event wording with an instructor or qualified analyst before applying the model to real observations.

Optional filing controls are a local prototype.

Checkout is unavailable. The reading above is complete; print, CSV and five local summaries are optional enhancements, not hidden answers.

Before using the draw-probability dial

Assume every subset of the stated draw size is equally likely and objects are not replaced between draws. The marked classification must be fixed before drawing, and each physical object appears once in the pool. This is not a model for biased selection, changing populations or independent trials with replacement. Whole pool size is supported from one through five hundred, marked count from zero through pool size and draw count from zero through pool size. The requirement may exceed feasible successes, which yields a clear zero rather than an input crash. Log-factorial combination arithmetic keeps intermediate counts from overflowing, while the displayed result is a probability estimate rounded for presentation, not a simulation or a prediction of the next draw.

Boundary and sources

Finite-pool probability exercise only, not a prediction, gambling strategy or proof that an observed selection was fair. Confirm the sampling mechanism and event wording with an instructor or qualified analyst before applying the model to real observations.

Mechanism: competence-autonomy-loop

Optional AI formatting, never the calculation

Manual entry completes this draw-probability dial for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.

Format only these fictional or non-sensitive notes for a draw-probability dial. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string", "string", "string"]}], "setting": "string"}. The columns are Pool code | total objects | marked objects | objects drawn; the setting is At least this many marked objects. Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.

An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.