When to use this calculator
Calculate the probability of at least one success in independent identical trials. Trials must be independent and use the same success probability.
Explore the probability & distributions calculators for other questions in this topic. For a related calculation, use the Bayes Theorem Calculator: Update a prior probability using likelihoods for evidence under two alternatives.
PUTTING IT INTO PRACTICE
At Least One Event: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Success probability per trial (%) | 10 |
| Number of trials (integer) | 5 |
| Result | 40.951 % |
- Check the input labels and enter the example values above.
- Apply the relationship: Probability (%) = (1 − (1 − p/100)^n) × 100.
- The result is 40.951 %, rounded for display.
How to interpret your result
Trials must be independent and use the same success probability.
A distribution model is an assumption about the process, not a guarantee about outcomes. Independence, constant probability and fixed interval definitions matter. Exactly-k probabilities differ from cumulative probabilities.
Frequently asked questions
Does exactly two successes mean two or more?
No. Exactly two counts only outcomes with two successes. Two or more is a cumulative probability covering several counts.
How do I use the at least one event calculator?
Enter success probability per trial (%), number of trials (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Probability (%) = (1 − (1 − p/100)^n) × 100.
What should I check before using the result?
Trials must be independent and use the same success probability.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: probability distributions ↗. This is a topic reference, not an external review or endorsement of this tool.
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