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THE FEUTEX TOOLKIT

Geometric Waiting-Time Probability

Calculate exact and cumulative waiting probabilities before the first successful trial.

Probability workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaExact = p*(1-p)**k; Cdf = 1-(1-p)**(k+1); Mean Failures = (1-p)/p; Variance = (1-p)/p**2
Sources and model references

Worked example

Inputs

Success probability
0.25 probability
Failures before success
3 integer

Expected results

Exact
0.10546875 probability
Cdf
0.68359375 probability
Mean Failures
3 number
Variance
12 number

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

How to use this tool

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

Try this example

{
  "p": 0.25,
  "k": 3
}

Accuracy and scope

Counts failures before the first success in independent identical trials. 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.