THE FEUTEX TOOLKIT

Random Bin Occupancy

Estimate occupied, empty and singleton bins after independent uniform assignments.

Probability workspace● Runs in your browser

01 Your input

Independent itemsitemsEqual-probability binsbins

02 Your result

View or copy raw result data

Result data

FormulaExpected Occupied = m*(1-(1-1/m)**n); Expected Empty = m*(1-1/m)**n; Expected Singletons = n*(1-1/m)**max(0,n-1)

Sources and model references

https://mathworld.wolfram.com/OccupancyProblem.html

Worked example

Inputs

Independent items: 10 items
Equal-probability bins: 5 bins

Expected results

Expected Occupied: 4.463129088 bins
Expected Empty: 0.536870912 bins
Expected Singletons: 1.34217728 bins

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

Enter the labeled inputs using consistent units.
Check the stated assumptions and calculate.
Review each output and compare another input scenario.

Try this example

{
  "n": 10,
  "m": 5
}

Accuracy and scope

Each item independently chooses a bin uniformly; outputs expectations, not guaranteed counts. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.