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THE FEUTEX TOOLKIT

Trials until Multiple Successes

Estimate trial count and variability required to reach multiple independent successes.

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

Worked example

Inputs

Required successes
5 count
Success chance per trial
0.25 probability

Expected results

Mean Trials
20 trials
Variance Trials
60 trials²
Mean Failures
15 failures

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

{
  "r": 5,
  "p": 0.25
}

Accuracy and scope

Independent constant-probability trials; total trials include the final success. 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.