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Statistics · Probability

Repeated Event Probability Calculator

Analyze an independent event across repeated trials and reverse-solve how many trials reach a selected at-least-once probability.

Statistics · Probability

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
The filled share represents the entered event probability on a zero-to-one scale.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Understand the probability

What the repeated event probability calculator is calculating

Counting outcomes across repeated trials. Repeated-event probability combines the count of qualifying outcome sequences with the probability of each sequence. Replacement and dependence determine whether trial probabilities stay fixed.

Probability rule

P(at least once)=1−(1−p)^n; minimum n=ceil[ln(1−target)/ln(1−p)].

Every probability must remain between 0 and 1, and overlapping regions must be jointly feasible. The calculator rejects combinations that violate the stated model.

How to interpret it

More trials increase the chance of at least one event but do not guarantee when it occurs or make dependent trials independent.

Model boundary: Every trial must be independent with the same event probability; target is used only for the reverse at-least-once calculation.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the repeated event probability calculator works

P(at least once)=1−(1−p)^n; minimum n=ceil[ln(1−target)/ln(1−p)].

More trials increase the chance of at least one event but do not guarantee when it occurs or make dependent trials independent.

Worked example

Repeated Event Probability example

With p=0.2 over 5 independent trials, the probability of at least one occurrence is 1−0.8⁵=0.67232.

P(at least once)=1−(1−p)^n; minimum n=ceil[ln(1−target)/ln(1−p)].

Supported inputs

Precision and limits

Model and design

Every trial must be independent with the same event probability; target is used only for the reverse at-least-once calculation.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

More trials increase the chance of at least one event but do not guarantee when it occurs or make dependent trials independent.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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