Random Urn Sampling Experiment Generator
Sample explicit physical urn items with caller replacement convention. Labels may repeat; distinct indices, not colors, are the no-replacement unit. Unused physical inventory retained.
Description
An urn inventory represents physical items whose labels may repeat.
An urn inventory represents physical items whose labels may repeat.1
Sampling distinct item positions preserves repeated colors or labels as valid outcomes.
When to use Random Urn Sampling Experiment Generator
Use this tool when you need to produce the reproducible draw or model experiment described below. Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
How to use Random Urn Sampling Experiment Generator and understand its results
- Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
- Enter seed, count, withoutReplacement, physicalItemLabels, following the field table and calculation rules below, then run the tool.
- Read result. Inspect the nested fields in the output table below and keep any missing evidence or selected indices visible.
- Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| seed | Nonblank reproducibility seed; default seeded runs restart for each request | string | Required |
| count | Number of simulated replicates | safe integer from 1 to 64 | Required |
| withoutReplacement | True draws distinct entry positions; false permits repeated positions | boolean | Required |
| physicalItemLabels | Physical item labels | list of string | Required |
Supply a nonempty list of nonblank physical-item labels, allowing duplicates. Apply the common sampling rules below to positions, return drawn labels and original indices, tally drawn labels in first-occurrence order, and list every undrawn original index. With replacement, undrawn means never selected rather than remaining quantity after a draw.2, 3
Use a nonblank seed of at most 256 UTF-16 units and a safe-integer count from 1 to 64. By default the seed is hashed into a deterministic pseudorandom state; each run restarts that state, so identical full inputs and implementation reproduce the result. The SDK may provide context.random, which replaces the seeded source and advances across the request; the seed remains required. Every source value must be finite in [0,1), with a request limit of 100000 source calls. Draw an index as floor(U×remainingSize). With replacement draw from the full inventory each time; without replacement remove each chosen position from an ordered pool and reject counts exceeding the inventory size. Uniform-source draws are over positions, not necessarily distinct values. This is not secure randomness.
drawCount(label)=count(selected positions bearing label) Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the fields below | object |
| result.drawnLabels | Drawn Labels | list |
| result.physicalItemIndices | Zero-based physical urn positions, allowing repeated labels | list |
| result.drawnLabelCounts | Drawn Label Counts | list |
| result.undrawnPhysicalItemIndices | Undrawn Physical Item Indices | list |
{
"input": {
"seed": "tool.io/batch42",
"count": 1,
"withoutReplacement": true,
"physicalItemLabels": [
"red",
"red",
"blue"
]
},
"output": {
"result": {
"drawnLabels": [
"blue"
],
"physicalItemIndices": [
2
],
"drawnLabelCounts": [
{
"label": "blue",
"count": 1
}
],
"undrawnPhysicalItemIndices": [
0,
1
]
}
}
}Limitations and assumptions
The default source is deterministic pseudorandomness, not an independently audited or secure draw. Replacement applies to inventory positions; distinct positions may render identically or yield equal answers. Review the supplied inventory or scenario domain independently before interpreting the sample.
Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Arrays must be dense, with no missing cells. Ordinary string lists allow at most 128 strings of at most 128 UTF-16 units each. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related task, use Random Raffle Draw Generator: A raffle inventory consists of distinct eligible tickets rather than distinct people. Sampling tickets without replacement can still award multiple prizes to one person holding several eligible tickets. For a complementary step, use Random Mahjong Practice Draw Generator: A teaching mahjong inventory can represent four physical copies of each selected tile type. Drawing distinct physical positions permits repeated tile glyphs without replacement.
References
-
Random Urn Sampling Experiment Generator — tool.io
-
Calculation or validation: random/number — tool.io
Similar or alternative tools
- Random Raffle Draw Generator
A raffle inventory consists of distinct eligible tickets rather than distinct people. Sampling tickets without replacement can still award multiple prizes to one person holding several eligible tickets.
- Random Mahjong Practice Draw Generator
A teaching mahjong inventory can represent four physical copies of each selected tile type. Drawing distinct physical positions permits repeated tile glyphs without replacement.